# Everyday Math Grade 4 Answers Unit 5 Fraction and Mixed-Number Computation; Measurement

## Everyday Mathematics 4th Grade Answer Key Unit 5 Fraction and Mixed-Number Computation; Measurement

Decomposing Fractions

Family Note In class today your child learned to decompose fractions into smaller parts.
For example, $$\frac{5}{6}$$ can be decomposed into $$\frac{1}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ , $$\frac{2}{6}$$ + $$\frac{3}{6}$$, $$\frac{1}{6}$$ + $$\frac{4}{6}$$, and so on.

Question 1.

Explanation :
$$\frac{11}{5}$$ is decomposed into different smaller fractions and combined as shown in the above figure .

Question 2.

Explanation :
$$\frac{11}{8}$$ is decomposed into different smaller fractions and combined as shown in the above figure .

3. Decompose $$\frac{8}{12}$$ in more than one way into a sum of fractions with the same denominator.
Record each decomposition with an equation and justify it by shading the circle.
a. Equation: ___

Equation : $$\frac{4}{12}$$ + $$\frac{4}{12}$$ = $$\frac{8}{12}$$

Explanation :
Given Circle is divided into 12 parts . Each part is a fraction of $$\frac{1}{12}$$ so, to form $$\frac{8}{12}$$ it is decomposed into $$\frac{4}{12}$$ + $$\frac{4}{12}$$ where, 2 – 4 parts are coloured in different colors as shown in above figure .

b. Equation: ___

Equation : $$\frac{2}{12}$$ + $$\frac{2}{12}$$ + $$\frac{2}{12}$$ + $$\frac{2}{12}$$ = $$\frac{8}{12}$$

Explanation :
Given Circle is divided into 12 parts . Each part is a fraction of $$\frac{1}{12}$$ so, to form $$\frac{8}{12}$$ it is decomposed into $$\frac{2}{12}$$ + $$\frac{2}{12}$$ + $$\frac{2}{12}$$ + $$\frac{2}{12}$$ where, 4 – 2 parts are coloured in different colors as shown in above figure .

Practice

Question 4.
9 âˆ— 785 = ___
9 âˆ— 785 = 7065
Explanation :

Step I:Â Arrange the numbers vertically.
Step II: First multiply the digit at the ones place by 9.
5 Ã— 9 = 45 = 4 ten + 5 ones
Write 5 in the ones column and carry 4 ten to tens place.
Step III: Multiply the digit at the tens place by 9.
8 Ã— 9 = 72 tens
72 + 4 (carried) = 76 tens = 7 hundreds + 6 ten
Write 6 in ten place and carry 7 hundreds to hundreds place.
Step IV: Multiply the digit at hundreds place by 9
7 hundred Ã— 9 = 63 hundreds
63 hundreds + 7 hundreds (carried) = 80 hundreds =8 thousands + 0 hundreds
Write 0 in hundreds place and carry 8 thousands to the thousands place .

Question 5.
461 âˆ— 7 = ___
461 âˆ— 7 = 3227
Explanation :

Step I:Â Arrange the numbers vertically.
Step II: First multiply the digit at the ones place by 7.
1 Ã— 7 = 7
Write 7 in the ones column .
Step III: Multiply the digit at the tens place by 7.
6 Ã— 7 = 42 tens
42 tens = 4 hundreds + 2 ten
Write 2 in ten place and carry 4 hundreds to hundreds place.
Step IV: Multiply the digit at hundreds place by 7
4 hundred Ã— 7 = 28 hundreds
28 hundreds + 4 hundreds (carried) = 32 hundreds = 3 thousands + 2 hundreds
Write 2 in hundreds place and carry 3 thousands to the thousands place .

Question 6.
644 âˆ— 4 = ___
644 âˆ— 4 = 2576
Explanation :

Step I:Â Arrange the numbers vertically.
Step II: First multiply the digit at the ones place by 4.
4 Ã— 4 = 16 = 1 ten + 6 ones
Write 6 in the ones column and carry 1 ten to tens place.
Step III: Multiply the digit at the tens place by 4.
4 Ã— 4 = 16 tens
16 + 1 (carried) = 17 tens = 1 hundreds + 7 ten
Write 7 in ten place and carry 1 hundreds to hundreds place.
Step IV: Multiply the digit at hundreds place by 4
6 hundred Ã— 4 = 24 hundreds
24 hundreds + 1 hundreds (carried) = 25 hundreds =2 thousands + 5 hundreds
Write 5 in hundreds place and carry 2 thousands to the thousands place .

Question 7.
___ = 39 âˆ— 50
1950 =Â 39 âˆ— 50

Explanation :
Step I: Arrange the numbers vertically.
Step II: Multiply 39 by 0 ones
39 Ã— 0 = 00
Step III: Multiply 39 by 5 tens
39 Ã— 50 = 1950
00 + 1950 = 1950

What Is the Whole?

For Problems 1-3, use your Geometry Template or sketch the shapes.

Question 1.
Suppose is is $$\frac{1}{4}$$. Draw each of the following:

Explanation :
Each is $$\frac{1}{4}$$ so,
To represent 1, 4 are drawn .
To represent 1 $$\frac{1}{2}$$, 6 are drawn .
To represent 2, 8 are drawn .

Question 2.
Suppose is $$\frac{2}{3}$$. Draw each of the following:
a. $$\frac{1}{3}$$
b. 1
c. $$\frac{4}{3}$$
d. 2

Suppose is $$\frac{2}{3}$$ then half of is $$\frac{1}{3}$$ .
Explanation :
Each is $$\frac{2}{3}$$ so,
a. To represent $$\frac{1}{3}$$, half ofÂ  is drawn .
b. To represent 1, 1 and half Â are drawn .
c. To represent $$\frac{4}{3}$$, 2Â  are drawn .
d. To represent 2, 3 Â are drawn .

Question 3.
Suppose is $$\frac{1}{3}$$. Draw each of the following:
a. $$\frac{3}{3}$$
b. 2
c. $$\frac{5}{3}$$
d. 1$$\frac{1}{3}$$

Explanation :
Each is $$\frac{1}{3}$$ so,
a. To represent $$\frac{3}{3}$$, 3 are drawn .
b. To represent 2, 6 Â are drawn .
c. To represent $$\frac{5}{3}$$, 5Â  Â are drawn .
d. To represent 1 $$\frac{1}{3}$$ , 4 Â are drawn .

Practice

Question 4.

$$\frac{4}{5}$$ = $$\frac{8}{10}$$.
Explanation :
$$\frac{4}{5}$$ = $$\frac{4 Ã— 2}{5 Ã— 2}$$ = $$\frac{8}{10}$$
Multiply numerator and denominator by 2 .

Question 5.

$$\frac{3}{4}$$ = $$\frac{9}{12}$$.
Explanation :
$$\frac{9}{12}$$ = $$\frac{9 Ã· 3}{12 Ã· 3}$$ = $$\frac{3}{4}$$
Divide numerator and denominator by 3 .

Question 6.

$$\frac{9}{10}$$ = $$\frac{90}{100}$$.
Explanation :
$$\frac{9}{10}$$ = $$\frac{9 Ã— 10}{10 Ã— 10}$$ = $$\frac{90}{100}$$
Multiply numerator and denominator by 10 .

Solve the number stories. Use a different strategy for each one.

Question 1.
The park department wants to have new trees planted. They agreed that $$\frac{1}{10}$$ of the trees will be oak, $$\frac{3}{10}$$ will be pine, and $$\frac{2}{10}$$ will be willow. They are undecided about the rest. What fraction of the trees will be oak, willow, or pine?
a. Fill in the whole box.

b. Number model with unknown:
Number of oak trees = $$\frac{1}{10}$$
Number of oak trees = $$\frac{3}{10}$$
Number of oak trees =Â  $$\frac{2}{10}$$
Total Trees = $$\frac{1}{10}$$ + $$\frac{3}{10}$$ + $$\frac{2}{10}$$ = $$\frac{6}{10}$$

c. One way to solve a fraction addition problem:

fraction is represented as $$\frac{6}{10}$$ that means total is 10

Number of oak trees = $$\frac{1}{10}$$
Number of oak trees = $$\frac{3}{10}$$
Number of oak trees =Â  $$\frac{2}{10}$$
Total Trees = $$\frac{1}{10}$$ + $$\frac{3}{10}$$ + $$\frac{2}{10}$$ = $$\frac{6}{10}$$ oak, willow, or pine trees .

Question 2.
The Patels have a DVD collection. Three-eighths of the DVDs are animated. Two-eighths of them are mysteries. One-eighth are comedies. The rest are about travel. What fraction of the DVDs are not about travel?
a. Fill in the whole box.

b. Number model with unknown:
Total Fraction = $$\frac{8}{8}$$
Fraction of DVDs are animated = $$\frac{3}{8}$$
Fraction of DVDs are mysteries = $$\frac{2}{8}$$
Fraction of DVDs are comedies = $$\frac{1}{8}$$
Fraction of DVDs that are not about travel =Â  $$\frac{3}{8}$$ + $$\frac{2}{8}$$ – $$\frac{1}{8}$$ = $$\frac{8}{8}$$ – $$\frac{6}{8}$$ = $$\frac{2}{8}$$ = $$\frac{1}{4}$$ DVD’S .

c. A different way to solve a fraction addition problem:

Explanation :
The Denominator of the Fraction represent the total as Eight .

Total Fraction = $$\frac{8}{8}$$
Fraction of DVDs are animated = $$\frac{3}{8}$$
Fraction of DVDs are mysteries = $$\frac{2}{8}$$
Fraction of DVDs are comedies = $$\frac{1}{8}$$
Fraction of DVDs that are not about travel =Â  $$\frac{3}{8}$$ + $$\frac{2}{8}$$ + $$\frac{1}{8}$$ = $$\frac{6}{8}$$ = $$\frac{3}{4}$$ DVD’SAdd.

Question 3.
$$\frac{2}{5}$$ + $$\frac{1}{5}$$ = ___
$$\frac{2}{5}$$ + $$\frac{1}{5}$$ = $$\frac{3}{5}$$

Question 4.
$$\frac{1}{2}$$ + $$\frac{3}{2}$$ = ___
$$\frac{1}{2}$$ + $$\frac{3}{2}$$ = $$\frac{4}{2}$$ = 2

Question 5.
$$\frac{5}{6}$$ + $$\frac{5}{6}$$ = ___
$$\frac{5}{6}$$ + $$\frac{5}{6}$$ = $$\frac{10}{6}$$ = $$\frac{5}{3}$$ = 1$$\frac{2}{3}$$

Question 6.
$$\frac{1}{3}$$ + $$\frac{2}{3}$$ + $$\frac{1}{3}$$ = ___
$$\frac{1}{3}$$ + $$\frac{2}{3}$$ + $$\frac{1}{3}$$ = $$\frac{4}{3}$$ = 1$$\frac{1}{3}$$

Practice

Represent the fractions as decimals.

Question 7.
$$\frac{4}{10}$$ = ___
$$\frac{4}{10}$$ = 0.4
Explanation :
Since theÂ denominator 10Â has a single zero, we shift theÂ decimal point in 4.0 one place to the left and get . 4 or 0.4 as the answer

Question 8.
$$\frac{40}{100}$$ = ___
$$\frac{40}{100}$$ = 0.04
Explanation :
Since the denominator 100 has two zero’s, we shift the decimal point in 40.0 two place to the left and get . 04 or 0.04 as the answer

Question 9.
$$\frac{6}{10}$$ = __
$$\frac{6}{10}$$ = 0.6
Explanation :
Since the denominator 10 has a single zero, we shift the decimal point in 6.0 one place to the left and get .6 or 0.6 as the answer

Question 10.
$$\frac{6}{100}$$ = ___
$$\frac{60}{100}$$ = 0.06
Explanation :
Since the denominator 100 has two zero’s, we shift the decimal point in 60.0 two place to the left and get . 06 or 0.06 as the answer

Solve the number stories. Use a different strategy for each one.

Question 1.
The art class had a box filled with balls of yarn. The students used 6$$\frac{2}{3}$$ balls for a project. There are now 2$$\frac{2}{3}$$ balls left in the box. How many balls of yarn did the art class start with?
a. Fill in the whole box.

b. Number model with unknown:
Number of yarn balls used for project = 6$$\frac{2}{3}$$ = $$\frac{20}{3}$$ .
Number of yarn balls left = 2$$\frac{2}{3}$$ = $$\frac{8}{3}$$ .
Total Number of yarn balls = $$\frac{20}{3}$$ + $$\frac{8}{3}$$ = $$\frac{28}{3}$$ = 9$$\frac{1}{3}$$ .

c. One way to solve a mixed-number addition problem:
I decomposed the mixed numbers so, First combine the wholes and then fractions
6$$\frac{2}{3}$$ + 2$$\frac{2}{3}$$ = 6 + $$\frac{2}{3}$$ + 2 + $$\frac{2}{3}$$ = 8 + $$\frac{4}{3}$$ = 9 + $$\frac{1}{3}$$ = 9$$\frac{1}{3}$$ .

Number of yarn balls used for project = 6$$\frac{2}{3}$$ = $$\frac{20}{3}$$ .
Number of yarn balls left = 2$$\frac{2}{3}$$ = $$\frac{8}{3}$$ .
Total Number of yarn balls = $$\frac{20}{3}$$ + $$\frac{8}{3}$$ = $$\frac{28}{3}$$ = 9$$\frac{1}{3}$$ .
Therefore, Total Number of yarn balls = 9$$\frac{1}{3}$$ balls .

Question 2.
Mrs. Meyers is growing vines along the sides of her house. On the west side the vines are 2$$\frac{4}{10}$$ meters tall. On the east side the vines are 5$$\frac{8}{10}$$ meters taller than the ones on the west side. How tall are the vines on the east side?

a. Fill in the whole box.

b. Number model with unknown:
Fraction of growing vines taller on west side = 2$$\frac{4}{10}$$ tall
Fraction of growing vines taller on east side = 5$$\frac{8}{10}$$ meters taller than the ones on the west side. = 5$$\frac{8}{10}$$Â  + 2$$\frac{4}{10}$$ = 5 + $$\frac{8}{10}$$ + 2 + $$\frac{4}{10}$$ = 7 + $$\frac{12}{10}$$ = 8 + $$\frac{2}{10}$$ = 8$$\frac{2}{10}$$ = 8$$\frac{1}{5}$$ meters .
Therefore, Fraction of growing vines taller on east side = 8$$\frac{2}{10}$$ = 8$$\frac{1}{5}$$ meters .

c. A different way to solve a mixed-number addition problem:
I decomposed the mixed numbers so, First combine the wholes and then fractions
5$$\frac{8}{10}$$Â  + 2$$\frac{4}{10}$$ = 5 + $$\frac{8}{10}$$ + 2 + $$\frac{4}{10}$$ = 7 + $$\frac{12}{10}$$ = 8 + $$\frac{2}{10}$$ = 8$$\frac{2}{10}$$ = 8$$\frac{1}{5}$$ meters .

Fraction of growing vines taller on west side = 2$$\frac{4}{10}$$ tall
Fraction of growing vines taller on east side = 5$$\frac{8}{10}$$ meters taller than the ones on the west side. = 5$$\frac{8}{10}$$Â  + 2$$\frac{4}{10}$$ = 5 + $$\frac{8}{10}$$ + 2 + $$\frac{4}{10}$$ = 7 + $$\frac{12}{10}$$ = 8 + $$\frac{2}{10}$$ = 8$$\frac{2}{10}$$ = 8$$\frac{1}{5}$$ meters .
Therefore, Fraction of growing vines taller on east side = 8$$\frac{2}{10}$$ = 8$$\frac{1}{5}$$ meters .

Question 3.
5$$\frac{2}{6}$$ + 3$$\frac{1}{6}$$ = ___
5$$\frac{2}{6}$$ + 3$$\frac{1}{6}$$ = $$\frac{32}{6}$$ + $$\frac{19}{6}$$ = $$\frac{51}{6}$$ = $$\frac{17}{2}$$ = 8 $$\frac{1}{2}$$ .

Question 4.
1$$\frac{5}{8}$$ + 2$$\frac{3}{8}$$ = ___
1$$\frac{5}{8}$$ + 2$$\frac{3}{8}$$ = $$\frac{13}{8}$$ + $$\frac{19}{8}$$ = $$\frac{32}{8}$$ = 4 .

Question 5.
3$$\frac{3}{4}$$ + 2$$\frac{3}{4}$$ = ___
3$$\frac{3}{4}$$ + 2$$\frac{3}{4}$$ = $$\frac{15}{4}$$ + $$\frac{11}{4}$$ = $$\frac{26}{4}$$ = $$\frac{13}{2}$$ = 6$$\frac{1}{2}$$ .

Question 6.
3$$\frac{2}{5}$$ + 1$$\frac{4}{5}$$ + 2$$\frac{3}{5}$$ = ___
3$$\frac{2}{5}$$ + 1$$\frac{4}{5}$$ + 2$$\frac{3}{5}$$ = $$\frac{17}{5}$$ + $$\frac{9}{5}$$ + $$\frac{13}{5}$$ = $$\frac{39}{5}$$ =7$$\frac{4}{5}$$

Practice

Question 7.
837 âˆ— 6 = ___
837 âˆ— 6 = 5,022
Explanation :

Question 8.
__ = 468 âˆ— 5
2,340 = = 468 âˆ— 5
Explanation :

Question 9.
__ = 364 âˆ— 3
1,089 = = 364 âˆ— 3
Explanation :

Question 10.
56 âˆ— 70 = __
56 âˆ— 70 = 3,920
Explanation :

Question 1.
2 tenths + 15 hundredths
Equation (in words): _______
Equation (in words):
2 tenths + 15 hundredths = 20 hundredths + 15 hundredths = 35 hundredths

Question 2.
$$\frac{68}{100}$$ + $$\frac{3}{10}$$
Equation: ______
Equation: $$\frac{68}{100}$$ + $$\frac{3}{10}$$ = $$\frac{68}{100}$$ + $$\frac{30}{100}$$ = $$\frac{98}{100}$$ .

Question 3.
$$\frac{1}{10}$$ + $$\frac{50}{100}$$
Equation: ______
Equation: $$\frac{1}{10}$$ + $$\frac{50}{100}$$ = $$\frac{1}{10}$$ + $$\frac{5}{10}$$ = $$\frac{6}{10}$$

Question 4.
$$\frac{4}{10}$$ + $$\frac{60}{100}$$ + $$\frac{3}{10}$$ + $$\frac{81}{100}$$
Equation: ______
Equation: $$\frac{4}{10}$$ + $$\frac{60}{100}$$ + $$\frac{3}{10}$$ + $$\frac{81}{100}$$ = $$\frac{40}{100}$$ + $$\frac{60}{100}$$ + $$\frac{30}{100}$$ + $$\frac{81}{100}$$ = $$\frac{211}{100}$$ = 2$$\frac{11}{100}$$ .

Question 5.
1$$\frac{3}{10}$$ + 5$$\frac{64}{100}$$
Equation: ____
Equation: 1$$\frac{3}{10}$$ + 5$$\frac{64}{100}$$ = $$\frac{13}{10}$$ + $$\frac{564}{100}$$ = $$\frac{130}{100}$$ + $$\frac{564}{100}$$ = $$\frac{694}{100}$$ = 6$$\frac{94}{100}$$ .

Question 6.
3$$\frac{22}{100}$$ + 2$$\frac{8}{10}$$
Equation: ______
Equation: 3$$\frac{22}{100}$$ + 2$$\frac{8}{10}$$ = $$\frac{322}{100}$$ + $$\frac{18}{10}$$ = $$\frac{322}{100}$$ + $$\frac{180}{100}$$ = $$\frac{502}{100}$$ = 5 $$\frac{2}{100}$$

Question 7.
$$\frac{15}{10}$$ + $$\frac{78}{100}$$
Equation: ______
Equation: $$\frac{15}{10}$$ + $$\frac{78}{100}$$ = $$\frac{150}{100}$$ + $$\frac{78}{100}$$ =Â  $$\frac{228}{100}$$ = 2$$\frac{28}{100}$$

Question 8.
Nicholas shaded $$\frac{40}{100}$$ of his hundreds grid. Victor shaded $$\frac{5}{10}$$ of his grid.
How much did they shade in all? ____ of a grid
Fraction of grid shaded by Nicholas = $$\frac{40}{100}$$ = $$\frac{4}{10}$$ = 0.4
Fraction of grid shaded by Victor = $$\frac{5}{10}$$ = 0.5
0.5 > 0.4 that means Victor shaded more than Nicholas .
Total fraction of grid shaded by both =$$\frac{4}{10}$$ + $$\frac{5}{10}$$ = $$\frac{9}{10}$$ ofÂ  a grid .

Practice +

Write three equivalent fractions.

Question 9.
$$\frac{1}{2}$$ = ___
$$\frac{1}{2}$$ = $$\frac{2}{4}$$ = $$\frac{3}{6}$$ = $$\frac{4}{8}$$
Explanation :
Equivalent fractionsÂ are theÂ fractions that have different numerator and denominator but are equal to the same value .

Question 10.
$$\frac{1}{3}$$ = __
$$\frac{1}{3}$$ = $$\frac{2}{6}$$ =Â  $$\frac{3}{9}$$ =Â  $$\frac{4}{12}$$
Explanation :
Equivalent fractionsÂ are theÂ fractions that have different numerator and denominator but are equal to the same value .

Question 11.
$$\frac{1}{4}$$ = __
$$\frac{1}{4}$$ = $$\frac{2}{8}$$ = $$\frac{3}{12}$$ = $$\frac{4}{12}$$
Explanation :
Equivalent fractionsÂ are theÂ fractions that have different numerator and denominator but are equal to the same value .

Question 12.
$$\frac{1}{5}$$ =
$$\frac{1}{5}$$ = $$\frac{2}{10}$$ = $$\frac{3}{15}$$ = $$\frac{4}{20}$$
Explanation :
Equivalent fractionsÂ are theÂ fractions that have different numerator and denominator but are equal to the same value .

Fraction Error Finder

Consider this problem:
A king owns land outside of his castle.
He has partitioned the land to give as gifts to his 5 sons.

What fraction of the land did the king give to each of his sons?
Here is Zekeâ€™s solution:

Question 1.
Identify Zekeâ€™s two errors, correct them, and explain why your answer is correct.
Bill and Carl also received $$\frac{1}{8}$$ .
Explanation :
As per the above figure , Andy Got half of the whole = $$\frac{1}{2}$$
And other 4 sons received land from rest of the half .
Fraction of part Bill , Carl , Dirk and Evan received $$\frac{1}{4}$$ part of $$\frac{1}{2}$$ =Â  $$\frac{1}{4}$$ Ã—Â  $$\frac{1}{2}$$ = $$\frac{1}{8}$$ part .
Drik and Evan received in a Square area Where Bill and carl both land are in rectangle shape and diagonally intersected that means half of the rectangle area. so, all the land area is equally divided but in different shapes .

Question 2.
Write a fraction addition equation to represent the correct answers and show the sum of the pieces of land.
Fraction of the Andy land = $$\frac{1}{2}$$
Fraction of the Bill land = $$\frac{1}{8}$$
Fraction of the Carl land = $$\frac{1}{8}$$
Fraction of the Drik land = $$\frac{1}{8}$$
Fraction of the Evan land = $$\frac{1}{8}$$
Total Land = $$\frac{1}{2}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ .

Practice

Question 3.
8,936 + 6,796 = ___
8,936 + 6,796 = 15,732
Explanation :

Step 1
Add the 1s: 6 + 6 = 12.
12 ones = 1 ten and 2 ones
Write 2 in the 1s place below the line.
Write 1 above the digits in the 10s place.

Step 2
Add the 10s: 3 + 9 + 1 = 13
13 tens = 1 hundred + 3 tens
Write 3 in the 10s place below the line.
Write 1 above the digits in the 100s place.

Step 3
Add the 100s: 9 + 7 + 1 = 17
17 hundreds = 1 thousand + 7 hundred
Write 7 in the 100s place below the line.
Write 1 above the digits in the 1000s place.

Step 4
Add the 1000s: 8 + 6 + 1 = 15
15 thousands= 1 ten thousand + 7 thousand
Write 7 in the 1000s place below the line.
Write 1 above the digits in the 10000s place.
No values to add in the ten thousandâ€™s place so write 1 below the line in 10000s place .

Question 4.
635 – 392 = ___
635 – 392 = 243
Explanation :

Step 1:
Start with the ones. Subtract the ones. 5 – 3 = 2 ones .
Step 2:
Go to the tens. Trade 1 hundred for 10 tens. Subtract the tens. 3 + 10 = 13 . 13 – 9 = 4 tens
Step 3:
Go to the hundreds. We donâ€™t need to regroup, so just subtract 5 – 3 = 2 .

Question 5.
6,386 + 4,205 = ___
6,386 + 4,205 = 10,591
Explanation :

thousand

Step 1
Add the 1s: 6 + 5 = 11.
11 ones = 1 ten and 1 ones
Write 1 in the 1s place below the line.
Write 1 above the digits in the 10s place.

Step 2
Add the 10s: 8 + 0 + 1 = 9
Write 9 in the 10s place below the line.

Step 3
Add the 100s: 3 + 2 = 5
Write 5 in the 100s place below the line.

Step 4
Add the 1000s: 6 + 4 = 10.
10 thousands = 1 ten thousand Â and 1 thousand
Write 0 in the 1s place below the line.
Write 1 above the digits in the 10000s place.
No values to add in the ten thousandâ€™s place so write 1 below the line in 10000s place .

Question 6.
900 – 463 =
900 – 463 = 437
Explanation :

Step 1:
Step 2:
Go to the tens. Trade 1 hundred for 10 tens. Subtract the tens. 3 + 10 = 13 . 13 – 9 = 4 tens
Step 1:
Trade 1 from hundreds , we have
9 hundreds – 1 = 8 hundreds
0 tens + 10 tens = 10 tens .
Step 2 :
Trade 1 from tens , we have
10 tens – 1 = 9 tens
0 ones + 10 ones = 10 ones .
Step 3 :
Now subtract the values .we get differences as 437 .

Subtracting Fractions

Solve the number stories. Use a different strategy for each one.

Question 1.
Elijah still had $$\frac{4}{5}$$ of his allowance at the end of the month. Then he spent $$\frac{3}{5}$$ of his original allowance on a movie ticket and popcorn. How much of Elijahâ€™s allowance was left?
a. Fill in the whole box.
b. Number model with unknown: _____
c . One way to solve a fraction subtraction problem:
a .

b.
Total Allowances = $$\frac{4}{5}$$
Allowances spent on Movie and pop corn = $$\frac{3}{5}$$
Allowances left =Â  $$\frac{4}{5}$$Â  – $$\frac{3}{5}$$Â  = $$\frac{1}{5}$$
Therefore, allowances left = $$\frac{1}{5}$$ of his allowances .
c.

d.
Total Allowances = $$\frac{4}{5}$$
Allowances spent on Movie and pop corn = $$\frac{3}{5}$$
Allowances left =Â  $$\frac{4}{5}$$Â  – $$\frac{3}{5}$$Â  = $$\frac{1}{5}$$
Therefore, allowances left = $$\frac{1}{5}$$ of his allowances .

Question 2.
Kendraâ€™s computer battery had $$\frac{9}{10}$$ of a charge. After her sister Lydia borrowed the computer, the battery had $$\frac{3}{10}$$ of a charge left. How much of the battery charge did Lydia use?
a. Fill in the whole box.
b. Number model with unknown: ______
c. Another way to solve a fraction subtraction problem.
a.

b.
Total Battery charge = $$\frac{9}{10}$$
Charge left after lydia use = $$\frac{3}{10}$$
Charge used by lydia = $$\frac{9}{10}$$ – $$\frac{3}{10}$$ = $$\frac{6}{10}$$ = $$\frac{3}{5}$$ charge .
c.

d.
Total Battery charge = $$\frac{9}{10}$$
Charge left after lydia use = $$\frac{3}{10}$$
Charge used by lydia = $$\frac{9}{10}$$ – $$\frac{3}{10}$$ = $$\frac{6}{10}$$ = $$\frac{3}{5}$$ charge .
Therefore, Battery Charge used by lydia = $$\frac{6}{10}$$ = $$\frac{3}{5}$$ battery charge .

Subtract.

Question 3.
$$\frac{2}{2}$$ – $$\frac{1}{2}$$ = ___
$$\frac{2}{2}$$ – $$\frac{1}{2}$$ = $$\frac{1}{2}$$
Explanation :
$$\frac{2}{2}$$ – $$\frac{1}{2}$$ = Â $$\frac{1}{2}$$

Question 4.
$$\frac{11}{6}$$ – $$\frac{4}{6}$$ = ___
$$\frac{11}{6}$$ – $$\frac{4}{6}$$ = 1$$\frac{1}{6}$$
Explanation :
$$\frac{11}{6}$$ – $$\frac{4}{6}$$ = $$\frac{7}{6}$$ = 1$$\frac{1}{6}$$

Question 5.
___ = 1 – $$\frac{1}{5}$$
$$\frac{4}{5}$$ = 1 – $$\frac{1}{5}$$
Explanation :
1 – $$\frac{1}{5}$$ = $$\frac{5}{5}$$ – $$\frac{1}{5}$$ = $$\frac{4}{5}$$

Practice

Question 6.
8,936 + 6,796 = ____
8,936 + 6,796 = 15,732
Explanation :

Question 7.
____ = 4,635 – 2,392
2,243 = 4,635 – 2,392
Explanation :

Question 8.
___ = 46,386 + 4,205
50,591 = 46,386 + 4,205
Explanation :

Question 9.
65,900 – 48,463 = ___
65,900 – 48,463 = 17, 437 .
Explanation :

Mixed-Number Subtraction

Solve the number stories. Use a different strategy for each one.

Question 1.
The chocolate chip cake recipe calls for 3$$\frac{1}{3}$$ cups of milk. We only have 1$$\frac{2}{3}$$ cups at home. How much more milk do we need?
a. Fill in the whole box.
b. Number model with unknown: ______
c. One way to solve a mixed-number subtraction problem:
a .

b.
Quantity of Milk Required for Chocolate cake = 3$$\frac{1}{3}$$
Quantity of milk at home = 1$$\frac{2}{3}$$
Quantity of Mor milk required = 3$$\frac{1}{3}$$ – 1$$\frac{2}{3}$$ = 3 + $$\frac{1}{3}$$ – 1 – $$\frac{2}{3}$$ = 1 + $$\frac{4}{3}$$ – $$\frac{2}{3}$$ = 1 + $$\frac{2}{3}$$ = 1$$\frac{2}{3}$$
c.
First subtract the whole numbers and then subtract fractions .
$$\frac{1}{3}$$ – 1$$\frac{2}{3}$$ = 3 + $$\frac{1}{3}$$ – 1 – $$\frac{2}{3}$$ = 1 + $$\frac{4}{3}$$ – $$\frac{2}{3}$$ = 1 + $$\frac{2}{3}$$ = 1$$\frac{2}{3}$$
d.
Quantity of milk required = = 1 + $$\frac{2}{3}$$ = 1$$\frac{2}{3}$$ cups of milk .

Question 2.
Lourdes is listening to an audio book that is 9 hours long. She has listened for 6$$\frac{1}{6}$$ hours so far. How many hours of listening time are left?
a. Fill in the whole box.
b. Number model with unknown: ____
c. A different way to solve a mixed-number subtraction problem:
a.

b.
Time Required for listening to an audio book = 9 hours
Time spent in Reading = 6$$\frac{1}{6}$$ hours = $$\frac{37}{6}$$ hours
Time left in Reading = 9 – 6$$\frac{1}{6}$$ = 9 – 6 – $$\frac{1}{6}$$ = 3 – $$\frac{1}{6}$$ = 2 – $$\frac{6}{6}$$ – $$\frac{1}{6}$$ = 2 – $$\frac{5}{6}$$ = 2$$\frac{5}{6}$$ .
Therefore, Time left in Reading = 2$$\frac{5}{6}$$ hours .
c.
First subtract the whole numbers and then subtract fractions .
9 – 6$$\frac{1}{6}$$ = 9 – 6 – $$\frac{1}{6}$$ = 3 – $$\frac{1}{6}$$ = 2 – $$\frac{6}{6}$$ – $$\frac{1}{6}$$ = 2 – $$\frac{5}{6}$$ = 2$$\frac{5}{6}$$ .
d.
Time left in Reading = 2$$\frac{5}{6}$$ hours .

Question 3.
4$$\frac{1}{2}$$ – 3$$\frac{1}{2}$$ =
4$$\frac{1}{2}$$ – 3$$\frac{1}{2}$$ = 1
Explanation :
4$$\frac{1}{2}$$ – 3$$\frac{1}{2}$$ = $$\frac{9}{2}$$ – $$\frac{7}{2}$$ = $$\frac{2}{2}$$ = 1

Question 4.
___ = 5$$\frac{8}{12}$$ – 5$$\frac{3}{12}$$
$$\frac{5}{12}$$ = 5$$\frac{8}{12}$$ – 5$$\frac{3}{12}$$
Explanation :
5$$\frac{8}{12}$$ – 5$$\frac{3}{12}$$ = $$\frac{68}{12}$$ – $$\frac{63}{12}$$ = $$\frac{5}{12}$$

Question 5.
4$$\frac{2}{5}$$ – 1$$\frac{4}{5}$$ = ___
4$$\frac{2}{5}$$ – 1$$\frac{4}{5}$$ = 2$$\frac{3}{5}$$
Explanation :
4$$\frac{2}{5}$$ – 1$$\frac{4}{5}$$ = $$\frac{22}{5}$$ – $$\frac{9}{5}$$ = $$\frac{13}{5}$$ = 2$$\frac{3}{5}$$ .

Question 6.
__ = 9$$\frac{4}{10}$$ – 3$$\frac{8}{10}$$
5$$\frac{6}{10}$$ = 9$$\frac{4}{10}$$ – 3$$\frac{8}{10}$$
Explanation :
9$$\frac{4}{10}$$ – 3$$\frac{8}{10}$$ = $$\frac{94}{10}$$ – $$\frac{38}{10}$$ = $$\frac{56}{10}$$ = 5$$\frac{6}{10}$$ .

Practice

Question 7.
____ = 54 âˆ— 10
540 = 54 âˆ— 10
Explanation :
Any number number multiplied with 10 having single 0 then add one 0 on the right of the number that is 540 .

Question 8.
63 âˆ— 100 = ___
63 âˆ— 100 = 6300 .
Explanation :
Any number number multiplied with 100 having two 0’s then add two 0’s on the right of the number that is 6300 .

Question 9.
86 âˆ— 94 = ______
86 âˆ— 94 = 8,084
Explanation :

Step I:Â Arrange the numbers vertically.
Step II: Multiply 86 by 4 ones
86 Ã— 4 = 344
Step III: Multiply 94 by 9 tens
94 Ã— 90 = 7740
344Â  + 7740 = 8084

Question 10.
5,715 âˆ— 6 = ___
5,715 âˆ— 6 = 34,290
Explanation :
Step I:Â Arrange the numbers vertically.
Step II: First multiply the digit at the ones place by 4.
5 Ã— 6 = 30 = 3 ten + 0 ones
Write 0 in the ones column and carry 3 ten to tens place.
Step III: Multiply the digit at the tens place by 6.
1 Ã— 6 = 6 tens + 3 ( carried ) = 9 tens
Write 9 in ten place
Step IV: Multiply the digit at hundreds place by 6
7 hundred Ã— 6 = 42 hundreds
42 hundreds = 4 thousands + 2 hundreds
Write 2 in hundreds place carry 4 thousands to thousands place.
Step V: Multiply the digit at thousands place by 6.
5 thousands Ã— 6 = 30 thousands
30 + 3 (carried) = 33 thousands =Â  3 ten thousands + 3 thousands
Write 3 in thousands place and carry 3 ten thousands to ten thousands place.

Student Growth

Mrs. Welch surveyed her students about how much they had grown over the past year. This is the data she gathered.

Question 1.
Plot the data set on the line plot.

Explanation :
All the students grown height is marked in the graph .

Use the completed line plot to answer the questions.

Question 2.
What is the greatest number of inches a student grew in a year?
3$$\frac{1}{2}$$ = Greatest number of inches grown
$$\frac{1}{2}$$ = least number of inches grown

Question 3.
What is the difference between the greatest and the least number of inches grown? Number model with unknown: ___ Answer: ____ inch(es)
Greatest number of inches grown = 3$$\frac{1}{2}$$
Leastest number of inches grown = 3$$\frac{1}{2}$$
The difference between the greatest and the least number of inches grown =3$$\frac{1}{2}$$Â  – $$\frac{1}{2}$$ = 3 .

Practice

Circle the three equivalent fractions in each group.

Question 4.
$$\frac{1}{4}$$, $$\frac{3}{6}$$, $$\frac{1}{8}$$, $$\frac{2}{8}$$, $$\frac{3}{12}$$

Explanation :
Equivalent fractions are $$\frac{1}{4}$$ = $$\frac{2}{8}$$ = $$\frac{3}{12}$$ .

Question 5.
$$\frac{3}{4}$$, $$\frac{4}{8}$$, $$\frac{6}{8}$$, $$\frac{5}{6}$$, $$\frac{9}{12}$$

Explanation :
Equivalent fractions are $$\frac{3}{4}$$ = $$\frac{6}{8}$$ = $$\frac{9}{12}$$

Question 6.
$$\frac{2}{3}$$, $$\frac{1}{5}$$, $$\frac{4}{6}$$, $$\frac{7}{12}$$, $$\frac{8}{12}$$

Explanation :
Equivalent fractions are $$\frac{2}{3}$$, $$\frac{4}{6}$$ and $$\frac{8}{12}$$ .

Question 7.
$$\frac{1}{2}$$, $$\frac{5}{10}$$, $$\frac{4}{8}$$, $$\frac{7}{12}$$

Explanation :
Equivalent fractions are $$\frac{1}{2}$$, $$\frac{5}{10}$$ and $$\frac{4}{8}$$

Rotations

Family Note If your child needs help with the following problems, consider putting up signs in a room in your home to indicate the directions north, south, east, and west. Do the turns with your child. Please return this Home Link to school tomorrow.

Make the turns described below. Show which way you face after each turn by:

• Drawing a dot on the circle.
• Labeling the dot with a letter.

Example: Face north.
Do a $$\frac{1}{2}$$ turn counterclockwise.
On the circle, mark the direction you are facing with the letter A.

Question 1.
Face north. Do a $$\frac{1}{4}$$ turn clockwise. Mark the direction you are facing with the letter B.

Question 2.
Face north. Do a $$\frac{3}{4}$$ turn clockwise. Mark the direction you are facing with the letter C.

Question 3.
Face east. Do a $$\frac{1}{4}$$ turn counterclockwise. Mark the direction you are facing with the letter D.

Question 4.
Face west. Make less than a $$\frac{1}{4}$$ turn clockwise. Mark the direction you are facing with the letter E.

Question 5.
Face north. Make a clockwise turn that is more than a $$\frac{1}{2}$$ turn but less than a $$\frac{3}{4}$$ turn. Mark the direction you are facing with the letter E.

Explanation :
A point is marked between $$\frac{1}{2}$$ and $$\frac{3}{4}$$ in clockwise direction from North and Point E lies on this clock wise direction towards West .

Question 6.
Face north. Make a counter clock wise turn that is less than a $$\frac{1}{2}$$ turn but more than a $$\frac{1}{4}$$ turn. Mark the direction you are facing with the letter G.

Explanation :
A point is marked between $$\frac{1}{2}$$ and $$\frac{1}{4}$$ in a counter clock wise direction from North Point G is lies in this direction towards south .

Practice

Question 7.
85 âˆ— 50 = ___
85 âˆ— 50 = 4,250
Explanation :

Question 8.
416 âˆ— 6 = _____
416 âˆ— 6 = 2,496
Explanation :

Question 9.
___ = 597 âˆ— 4
2,376 = 597 âˆ— 4
Explanation :

Question 10.
1,373 âˆ— 7 = ___
1,373 âˆ— 7 = 9,611
Explanation :

Estimating Angle Measures

Family Note Our class has been learning about turns, angles, and angle measures. A full turn can be represented by an angle of 360Â°, a$$\frac{1}{2}$$ turn by an angle of 180Â°, a$$\frac{1}{4}$$ turn by an angle of 90Â°, and so on. Help your child match the measures below with the angles pictured. (It is not necessary to measure the angles with a protractor.)

Name which angle has the given measure.

Question 1.
Angle A

Question 2.
Angle D

Question 3.
Angle E

Question 4.
between 0Â° and 90Â° angle ___
Angle C

Question 5.
between 90Â° and 180Â° angle ____
Angle A or Angle B

Practice

Question 6.
5,956 + 4,983 = ___
5,956 + 4,983 = 10,939
Explanation :

Question 7.
60,351 + 86,037 = ___
60,351 + 86,037 = 1,46,388
Explanation :

Question 8.
41,015 – 517 = ___
41,015 – 517 = 40,498
Explanation :

Question 9.
23,730 – 10,769 = ____
23,730 – 10,769 = 12,961
Explanation :

Folding Shapes

Family Note Our class has been studying lines of symmetryâ€”lines that divide figures into mirror images. Help your child look for symmetric shapes in books, newspapers, and magazines, and in objects around the house, such as windows, furniture, dishes, and so on.

Question 1.
Fold a sheet of paper in half. Cut off the folded corner, as shown. Before you unfold the cutoff piece, guess its shape.
a. Unfold the cutoff piece. What shape is it?
________

b. How many sides of the cutoff piece are the same length? sides

c. How many angles are the same size? angles

d. The fold is a line of symmetry. Does the cutoff piece have any other lines of symmetry?

a. The shape of cutoff piece is triangle .
b. 2 sides of the cutoff piece are the same length.
c. 2 angles are the same size .
d. The fold is not a line of symmetry . The cutoff piece doesnot have any other lines of symmetry .

Question 2.
Fold another sheet of paper in half. Fold it in half again. Make a mark on both folded edges 2 inches from the folded corner. Cut off the folded corner. Before you unfold the cutoff piece, guess its shape.

a. Unfold the cutoff piece. What shape is it? ___
b. Are there any other lines of symmetry besides the fold lines?
c. On the back of this paper, draw a picture of the cutoff shape. Draw all of its lines of symmetry.

a. The shape of cutoff piece is triangle .
b. No
c. No, lines of symmentry .

Practice

Question 3.
81 Ã· __ = 9
81 Ã· 9 = 9
Explanation :
As we know , 9 Ã— 9 = 81

Question 4.
___ Ã· 9 = 6
54 Ã· 9 = 6
Explanation :
As we know , 9 Ã— 6 = 54

Question 5.
7 = 42 Ã· ___
7 = 42 Ã· 6
Explanation :
As we know , 7 Ã— 6 = 42

Question 6.
___ Ã· 9 = 8
72 Ã· 9 = 8
Explanation :
As we know , 9 Ã— 8 = 72

Question 7.
36 Ã· __ = 4
36 Ã· 9 = 4
Explanation :
As we know , 9 Ã— 4 = 36

Question 8.
8 = __ Ã· 6
8 = 48 Ã· 6
Explanation :
As we know , 8 Ã— 6 = 48

Family Note Today students learned to express solutions to multistep number stories using correct units and single number models. Have your child explain the steps for solving each of the problems below, and then help him or her write these steps as a single number model, including a letter for the unknown quantity.

Solve. Record a long number model with a letter for the unknown quantity and write the answer with the correct unit.

Question 1.
Guillermo hires two painters to paint the walls of his living room. The painters each make $42 an hour for an 8-hour workday. If the work takes 3 days, how much will Guillermo pay the painters? Number model with unknown: ___________ Estimate: __________ Answer (with unit): ________ Answer: Number of Painters = 2 Number of Hours painted for 1 day = 8 hours Number of hours painted for 3 days = 8 Ã— 3 = 24 hours Number ofÂ hours painted by 2 painters = 2 Ã— 24 = 48 hours Cost of one hour to paint =$42
Cost of 48 hours to paint = $42 Ã— 48 = 2016$
Estimation:
Number ofÂ  hours painted by 2 painters = 2 Ã— 24 = 48 hours ==>50 hours
Cost of one hour to paint = $42 ==>40 Cost of 48 hours to paint =$40 Ã— 50 = 2000 $Question 2. Blaine is on vacation in New York City and wants to collect magnets of places he visits to give to all his friends. The Times Square magnets cost$2 each and come in sets of 4. The Statue of Liberty magnets cost $3 each and come in sets of 5. If Blaine buys 12 sets of each type of magnet, how much will he pay? Number model with unknown: _______ Estimate: ______ Answer (with unit): ______ Cost of Each Times Square Magnets =$2
Number in one set= 4
Cost of each set = $2 Ã— 4 =$8
Cost of 12 sets of Times and Square Magnets = $8 Ã— 12 = 96$
Cost of Each Statue of Liberty Magnets = $3 Number in one set= 5 Cost of each set =$3 Ã— 5 = $15 Cost of 12 sets of Statue of Liberty Magnets =$15 Ã— 12 = 180 $Total cost = 96 + 180 = 276$
Estimation:
Cost of 12 sets of Times and Square Magnets = $8 Ã— 12 = 96$ ==>100$Cost of 12 sets of Statue of Liberty Magnets =$15 Ã— 12 = 180 $Total cost = 100 + 180 = 280$

Practice

Question 3.
45 Ã· 5 = ___
45 Ã· 5 = 9
Explanation :
As we know , 9 Ã— 5 = 45

Question 4.
56 Ã· 8 = ___
56 Ã· 8 = 7
Explanation :
As we know , 8 Ã— 7 = 56

Question 5.
54 Ã· 9 = ___
54 Ã· 9 = 6
Explanation :
As we know , 9 Ã— 6 = 54

Question 6.
__ Ã· 9 = 4
36 Ã· 9 = 4
Explanation :
As we know , 9 Ã— 4 = 36

Question 7.
__ Ã· 6 = 6