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## 180 Days of Math for Fifth Grade Answers Key Day 179

**Directions: Solve each problem.**

Question 1.

248 + 39 = ___________

Answer:

The addition is the term used to describe adding two or more numbers together. The addition is denoted using the plus sign ‘+‘ such as the addition of 3 and 3 can be written as 4 + 4. Also, the plus sign (+) can be used as many times as required, such as

4 + 4 + 4 + 4.

Therefore, the answer is 287.

Question 2.

93 × 54 = ___________

Answer: 5022

Explanation:

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life. The major application we can see in multiplication tables.

In arithmetic, the multiplication of two numbers represents the repeated addition of one number with respect to another. These numbers can be whole numbers, natural numbers, integers, fractions, etc. If m is multiplied by n, then it means either m is added to itself ‘n’ number of times or vice versa.

The formula for multiplication:

The multiplication formula is given by:

Multiplier × Multiplicand = Product

– The multiplicand is the total number of objects in each group

– A multiplier is the number of equal groups

– Product is the result of multiplication of multiplier and multiplicand

Therefore, the answer is 5022.

Question 3.

Answer:

The square root of a number is defined as the value, which gives the number when it is multiplied by itself. The radical symbol √ is used to indicate the square root. For example, √9 = 3. The radical symbol is also called a root symbol or surds. If a number is a perfect square, we can easily find the square root of the number. If the given number is not a perfect square number, the square root can be found using the long division method.

– Here we will show you how to calculate the square root of 891 using the long division method with one decimal place accuracy.

Step 1: Set up 891 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:

step 2: Starting with the first set: the largest perfect square less than or equal to 8 is 4, and the square root of 4 is 2. Therefore, put 2 on top and 4 at the bottom like this:

step 3: Calculate 8 minus 4 and put the difference below. Then move down the next set of numbers.

step 4: Double the number on top: 2 × 2 = 4. Then, use 4 and the bottom number to make this problem:

4? × ? ≤ 491

The question marks are “blank” and the same “blank”. With trial and error, we found the largest number “blank” can be is 9. Replace the question marks in the problem with 9 to get:

49 × 9 = 441.

Now, enter 9 on top, and 441 at the bottom:

step 5: Calculate 491 minus 441 and put the difference below. Then move down the next set of numbers.

step 6: Double the number in green on top: 29 × 2 = 58. Then, use 58 and the bottom number to make this problem:

58? × ? ≤ 5000

The question marks are “blank” and the same “blank”. With trial and error, we found the largest number “blank” can be is 8. Now, enter 8 on top:

The square root of 891 with one digit decimal accuracy is 29.8. You can add decimals by simply adding more sets of 00 and repeating the last two steps over and over.

The above-given question is 84 square root of 891

The square root of 891 is 29.8

Now multiply 84 and 29.8

Thus, 84 * 29.8 = 2503.2

Question 4.

Round 138,492 to the nearest thousand.

Answer: 138000

The above-given number is 138,492

The digit at the hundredth place of 138,492 is 4

That means 4 is less than 5.

So change digits at hundredth, tenth, and one’s place to zero.

Obtained rounded number for 138492 is 138000.

Question 5.

Write 2\(\frac{3}{4}\) as an improper fraction.

Answer:

2 3/4 is a mixed number, also known as a mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

2 = whole number

3 = numerator

4 = denominator

To convert mixed number 2 3/4 to an improper fraction, you follow these steps:

– Multiply the whole number by the denominator

2 × 4 = 8

– Add the product from Step 1 to the numerator

8 + 3 = 11

– Write answer from Step 2 over the denominator

11/4

The mixed number 2 3/4 converted to an improper fraction is, therefore :11/4

Question 6.

30 – (10 × 2) = _________

Answer:

The value of 10 × 2 = 20

30-20=10

Therefore, the answer is 20

Question 7.

Answer: 125

how 125 is the answer:

– What I have done is I subtracted 67 from 192 then we get 125.

– For re-verification 125+67 then we get 192.

Question 8.

8 cups = _________ pints

Answer:

8 cups are equal to 4 pints

The conversion factor from cups to pints is 0.5, which means that 1 cup is equal to 0.5 pints:

1 cup=0.5 pt

To convert 8 cups into pints we have to multiply 8 by the conversion factor in order to get the volume amount from cups to pints. We can also form a simple proportion to calculate the result:

We conclude that 8 cups is equivalent to 4 pints:

8 cups = 4 pints

Question 9.

Use a protractor to draw an acute angle.

Answer:

Acute angle comes under less than 90 degrees.

An angle is formed when two rays meet at a point. In the given figure, the point of intersection of the ray OA and ray OB is O, which is called the vertex.

If the measure of the angle formed by two rays is 30 degrees, then the angle is called a 30-degree angle. The angle formed by the ray OA and OB are written as ∠AOB or ∠BOA.

∠AOB=∠BOA=30°.

constructing 30 – degree angle using protractor:

step 1: Draw a line segment OA.

step 2: Place the centre tip of the protractor at point O such that the protractor perfectly aligns with line AO.

step 3: Start from ‘A’ on the protractor in the clockwise direction and stop at 30. Mark it as point ‘D’. If point ‘A’ lies to the right of ‘O’, then start measuring anticlockwise and stop at 30.

step 4: Joinpoint ‘D’ with ‘O’. ∠AOD=30° is the required 30-degree angle.

Question 10.

What is the median of this data set?

1,425; 1,595; 1,392; 1,436

Answer:

The median of a set of data is the middlemost number or centre value in the set. The median is also the number that is halfway into the set. To find the median, the data should be arranged, first, in order of least to greatest or greatest to the least value. A median is a number that is separated by the higher half of a data sample, a population or a probability distribution, from the lower half. The median is different for different types of distribution.

Now arrange the given numbers in ascending order:

1392, 1425, 1436, 1595

median=1425+1436/2

median=2861/2

median=1430.5

Therefore, the median of the data set is 1430.5

Question 11.

Imagine that you write each letter of the word CALIFORNIA on individual cards. You shuffle them, turn them facedown on a table, and turn over the top card. What is the probability of turning over a number?

Answer:

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event. For an experiment having ‘n’ number of outcomes, the number of favourable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

The given letter is CALIFORNIA

The total number of letters=10

Therefore, the total outcomes are 10

Turning over the top card=1

The favourable outcomes are 1.

According to the definition:

P(turning over a number)=1/10

Question 12.

How many squares of any size are there in the image?

Answer: 10 squares

The outer square is 1

The coloured squares are 4

The line was drawn those squares are 4

the line with red colour is 1

Now add all the numbers: 4+4+1+1=10

Therefore, in the above-given diagram, there are 10 squares are present.