All the solutions provided in McGraw Hill My Math Grade 4 Answer Key PDF Chapter 9 Check My Progress will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Chapter 9 Check My Progress Answer Key
Check My Progress Page No. (585 – 586)
Vocabulary Check
Question 1.
Circle the pair of like fractions.
Explain how you knew which pair of fractions to circle.
Answer:
The pair of like fractions: \(\frac{4}{6}\) and \(\frac{5}{6}\)
Explanation:
The group of two or more fractions that have exactly the same denominator are called like fractions.
Fractions with different denominators are called the unlike fractions.
\(\frac{4}{6}\) and \(\frac{5}{6}\) – Same denominators = like fractions.
\(\frac{1}{2}\) and \(\frac{3}{4}\) – Different denominators = Unlike fractions.
\(\frac{1}{3}\) and \(\frac{2}{6}\) – Different denominators = Unlike fractions.
\(\frac{1}{10}\) and \(\frac{2}{100}\) – Different denominators = Unlike fractions.
Concept Check
Algebra Write each fraction as a sum of unit fractions. Then write an equation to decompose the fraction into a different way.
Question 2.
\(\frac{4}{5}\)
Answer:
Equation to decompose the fraction into a different way:
\(\frac{4}{5}\) = \(\frac{2}{5}\) + \(\frac{2}{5}\)
Explanation:
In general, any unit fraction can be decomposed into the sum of two distinct unit fractions.
Decomposition of \(\frac{4}{5}\) into unit fractions:
\(\frac{4}{5}\) = \(\frac{2}{5}\) + \(\frac{2}{5}\)
Question 3.
\(\frac{3}{8}\)
Answer:
Equation to decompose the fraction into a different way:
\(\frac{3}{8}\) = \(\frac{1}{8}\) + \(\frac{5}{16}\)
Explanation:
Decomposition of \(\frac{3}{8}\) into unit fractions:
\(\frac{3}{8}\) = \(\frac{1}{8}\) + \(\frac{5}{16}\)
Find each sum. Write in simplest form.
Question 4.
\(\frac{2}{5}\) + \(\frac{2}{5}\) = _________________
Answer:
Sum of \(\frac{2}{5}\) and \(\frac{2}{5}\), we get \(\frac{4}{5}\).
Explanation:
Sum:
\(\frac{2}{5}\) + \(\frac{2}{5}\) = [(2 + 2) ÷ 5] = \(\frac{4}{5}\)
Simplest form:
\(\frac{4}{5}\) -Its already in Simplest form.
Question 5.
\(\frac{1}{8}\) + \(\frac{5}{8}\) = _________________
Answer:
Sum of \(\frac{1}{8}\) and \(\frac{5}{8}\), we get \(\frac{3}{4}\)
Explanation:
Sum:
\(\frac{1}{8}\) + \(\frac{5}{8}\) = [(1 + 5) ÷ 8] = \(\frac{6}{8}\)
Simplest form:
\(\frac{6}{8}\) = \(\frac{6}{8}\) ÷ \(\frac{2}{2}\) = \(\frac{3}{4}\)
Question 6.
\(\frac{2}{6}\) + \(\frac{1}{6}\) = _________________
Answer:
Sum of \(\frac{2}{6}\) and \(\frac{1}{6}\), we get \(\frac{1}{2}\)
Explanation:
Sum:
\(\frac{2}{6}\) + \(\frac{1}{6}\) = [(2 + 1) ÷ 6] = \(\frac{3}{6}\)
Simplest form:
\(\frac{3}{6}\) = \(\frac{3}{6}\) ÷ \(\frac{3}{3}\) = \(\frac{1}{2}\)
Find each difference. Write in simplest form.
Question 7.
\(\frac{7}{10}\) – \(\frac{4}{10}\) = _________________
Answer:
Difference between \(\frac{7}{10}\) and \(\frac{4}{10}\), we get \(\frac{3}{10}\)
Explanation:
Difference:
\(\frac{7}{10}\) – \(\frac{4}{10}\) = [(7 – 4) ÷ 10] = \(\frac{3}{10}\)
Simplest form:
\(\frac{3}{10}\) – Its already in its Simplest form.
Question 8.
\(\frac{3}{4}\) – \(\frac{1}{4}\) = _________________
Answer:
Difference between \(\frac{3}{4}\) and \(\frac{1}{4}\), we get \(\frac{1}{2}\)
Explanation:
Difference:
\(\frac{3}{4}\) – \(\frac{1}{4}\) = [(3 – 1) ÷ 4] = \(\frac{2}{4}\)
Simplest form:
\(\frac{2}{4}\) = \(\frac{2}{4}\) ÷ \(\frac{2}{2}\) = \(\frac{1}{2}\)
Question 9.
\(\frac{10}{12}\) – \(\frac{6}{12}\) = _________________
Answer:
Difference between \(\frac{10}{12}\) and \(\frac{6}{12}\), we get \(\frac{1}{3}\)
Explanation:
Difference:
\(\frac{10}{12}\) – \(\frac{6}{12}\) = [(10 – 6) ÷ 12] = \(\frac{4}{12}\)
Simplest form:
\(\frac{4}{12}\) = \(\frac{4}{12}\) ÷ \(\frac{4}{4}\) = \(\frac{1}{3}\)
Problem Solving
Question 10.
Elizabeth has \(\frac{7}{10}\) of a dollar. If she spends \(\frac{4}{10}\) of a dollar, what fraction of a dollar will she have left?
Answer:
Number of dollars she have left = \(\frac{3}{10}\)
Explanation:
Number of dollars Elizabeth has = \(\frac{7}{10}\)
Number of dollars she spends = \(\frac{4}{10}\)
Number of dollars she have left = Number of dollars Elizabeth has – Number of dollars she spends
= \(\frac{7}{10}\) – \(\frac{4}{10}\)
= \(\frac{3}{10}\)
Question 11.
A game uses tokens. Two-sixths of the tokens are blue. Three-sixths of the tokens are gold. What fraction of the tokens are either blue or gold?
Answer:
Fraction of the tokens are either blue or gold = \(\frac{1}{6}\)
Explanation:
Fraction of the tokens are blue = Two-sixths = \(\frac{2}{6}\)
Fraction of the tokens are gold = Three-sixths = \(\frac{3}{6}\)
Difference:
Fraction of the tokens are either blue or gold = Fraction of the tokens are gold – Fraction of the tokens are blue
= \(\frac{3}{6}\) – \(\frac{2}{6}\)
= [(3 – 2) ÷ 6]
= \(\frac{1}{6}\)
Question 12.
A glass has \(\frac{6}{8}\) cup of water. If Jack pours out \(\frac{3}{8}\) cup of the water, how much water will be left?
Answer:
Number of cups of water is left = \(\frac{3}{8}\)
Explanation:
Number of cups of water a glass has = \(\frac{6}{8}\)
Number of cups of water Jack pours out = \(\frac{3}{8}\)
Number of cups of water is left = Number of cups of water a glass has – Number of cups of water Jack pours out
= \(\frac{6}{8}\) – \(\frac{3}{8}\)
= [(6 – 3) ÷ 8]
= \(\frac{3}{8}\)
Question 13.
A recipe uses \(\frac{1}{4}\) cup of apple juice and \(\frac{2}{4}\) cup of orange juice. What is the total amount of apple juice and orange juice in the recipe?
Answer:
Total amount of apple juice and orange juice in the recipe = \(\frac{3}{4}\)
Explanation:
Number of cups of apple juice a recipe uses = \(\frac{1}{4}\)
Number of cups of orange juice a recipe uses = \(\frac{2}{4}\)
Total amount of apple juice and orange juice in the recipe = Number of cups of apple juice a recipe uses + Number of cups of orange juice a recipe uses
= \(\frac{1}{4}\) + \(\frac{2}{4}\)
= [(1 + 2) ÷ 4]
= \(\frac{3}{4}\)
Test Practice
Question 14.
What is the sum of \(\frac{2}{10}\) and \(\frac{3}{10}\) in the simplest form?
(A) \(\frac{5}{20}\)
(B) \(\frac{1}{10}\)
(C) \(\frac{23}{10}\)
(D) \(\frac{1}{2}\)
Answer:
Sum of \(\frac{2}{10}\) and \(\frac{3}{10}\) = \(\frac{5}{10}\) = \(\frac{1}{2}\)
(D) \(\frac{1}{2}\)
Explanation:
Sum of \(\frac{2}{10}\) and \(\frac{3}{10}\):
\(\frac{2}{10}\) and \(\frac{3}{10}\) = [(2 + 3) ÷ 10] = \(\frac{5}{10}\)
Simplest form of \(\frac{5}{10}\):
\(\frac{5}{10}\)= \(\frac{5}{10}\)÷ \(\frac{5}{5}\) = \(\frac{1}{2}\)
Check My Progress Page No. (605 – 606)
Vocabulary Check
Draw lines to match each of the following with its correct description or example.
Answer:
Explanation:
The group of two or more fractions that have exactly the same denominator are called like fractions.
A mixed number is a number consisting of a whole number and a proper fraction.
A fraction is in simplest form if the top and bottom have no common factors other than 1.
Concept Check
Find each sum. Write in simplest form.
Question 4.
1\(\frac{5}{10}\) + \(\frac{3}{10}\) = ________________
Answer:
Sum of 1\(\frac{5}{10}\) and \(\frac{3}{10}\), we get \(\frac{18}{10}\) = \(\frac{9}{5}\)
Explanation:
1\(\frac{5}{10}\) + \(\frac{3}{10}\) = {[(1 × 10) + 5] ÷ 10} + \(\frac{3}{10}\)
= [(10 + 5) ÷ 10] + \(\frac{3}{10}\)
= \(\frac{15}{10}\) + \(\frac{3}{10}\)
= (15 + 3) ÷ 10
= \(\frac{18}{10}\)
Simplest form:
\(\frac{18}{10}\) = \(\frac{18}{10}\) ÷ \(\frac{2}{2}\) = \(\frac{9}{5}\)
Question 5.
8\(\frac{8}{12}\) + 1\(\frac{1}{12}\) = ________________
Answer:
Sum of 8\(\frac{8}{12}\) and 1\(\frac{1}{12}\), we get \(\frac{39}{4}\)
Explanation:
8\(\frac{8}{12}\) + 1\(\frac{1}{12}\) = {[(8 × 12) + 8]÷ 12} + {[(1 × 12) + 1]÷ 12}
= [(96 + 8) ÷ 12] + [(12 + 1) ÷ 12]
= \(\frac{104}{12}\) + \(\frac{13}{12}\)
= (104 + 13) ÷ 12
= \(\frac{117}{12}\)
Simplest form:
\(\frac{117}{12}\) = \(\frac{117}{12}\) ÷ \(\frac{3}{3}\) = \(\frac{39}{4}\)
Question 6.
5\(\frac{1}{4}\) + 3\(\frac{1}{4}\) = ________________
Answer:
Sum of 5\(\frac{1}{4}\) and 3\(\frac{1}{4}\), we get \(\frac{17}{2}\)
Explanation:
5\(\frac{1}{4}\) + 3\(\frac{1}{4}\) = {[(5 × 4) + 1]÷ 4} + {[(3 × 4) + 1]÷ 4}
= [(20 + 1) ÷ 4] + [(12 + 1) ÷ 4]
= \(\frac{21}{4}\) + \(\frac{13}{4}\)
= (21 + 13) ÷ 4
= \(\frac{34}{4}\)
Simplest form:
\(\frac{34}{4}\) = \(\frac{34}{4}\) ÷ \(\frac{2}{2}\) = \(\frac{17}{2}\)
Question 7.
7\(\frac{20}{100}\) + 2\(\frac{40}{100}\) = _________________
Answer:
Sum of 7\(\frac{20}{100}\) and 2\(\frac{40}{100}\), we get \(\frac{48}{5}\)
Explanation:
7\(\frac{20}{100}\) + 2\(\frac{40}{100}\) = {[(7 × 100) + 20]÷ 100} + {[(2 × 100) + 40]÷ 100}
= [(700 + 20) ÷ 100] + [(200 + 40) ÷ 100]
= \(\frac{720}{100}\) + \(\frac{240}{100}\)
= (720 + 240) ÷ 100
= \(\frac{960}{100}\)
Simplest form:
\(\frac{960}{100}\) = \(\frac{960}{100}\) ÷ \(\frac{10}{10}\) = \(\frac{96}{10}\) ÷ \(\frac{2}{2}\) = \(\frac{48}{5}\)
Find each difference. Write in simplest form.
Question 8.
5\(\frac{7}{8}\) – 3\(\frac{2}{8}\) = _________________
Answer:
Difference between 5\(\frac{7}{8}\) and 3\(\frac{2}{8}\), we get \(\frac{21}{8}\)
Explanation:
Difference:
5\(\frac{7}{8}\) – 3\(\frac{2}{8}\) = {[(5 × 8) + 7] ÷ 8} – {[(3 × 8) + 2] ÷ 8}
= [(40 + 7) ÷ 8] – [(24 + 2) ÷ 8]
= \(\frac{47}{8}\) – \(\frac{26}{8}\)
= (47 – 26) ÷ 8
= \(\frac{21}{8}\) = Its in simplest form.
Question 9.
7\(\frac{2}{3}\) – 1\(\frac{1}{3}\) = ________________
Answer:
Difference between 7\(\frac{2}{3}\) and 1\(\frac{1}{3}\), we get \(\frac{19}{3}\)
Explanation:
Difference:
7\(\frac{2}{3}\) – 1\(\frac{1}{3}\) = {[(7 × 3) + 2] ÷ 3} – {[(1 × 3) + 1] ÷ 3}
= [(21 + 2) ÷ 3] – [(3 + 1) ÷ 3]
= \(\frac{23}{3}\) – \(\frac{4}{3}\)
= (23 – 4) ÷ 3
= \(\frac{19}{3}\) = Its in simplest form.
Question 10.
9\(\frac{11}{12}\) – 4\(\frac{1}{12}\) = _________________
Answer:
Difference between 9\(\frac{11}{12}\) and 4\(\frac{1}{12}\), we get \(\frac{35}{6}\)
Explanation:
Difference:
9\(\frac{11}{12}\) – 4\(\frac{1}{12}\) = {[(9 × 12) + 11] ÷ 12} – {[(4 × 12) + 1] ÷ 12}
= [(108 + 11) ÷ 12] – [(48 + 1) ÷ 12]
= \(\frac{119}{12}\) – \(\frac{49}{12}\)
= (119 – 49) ÷ 12
= \(\frac{70}{12}\)
Simplest form:
\(\frac{70}{12}\) = \(\frac{70}{12}\) ÷ \(\frac{2}{2}\) = \(\frac{35}{6}\)
Question 11.
3\(\frac{60}{100}\) – 1\(\frac{20}{100}\) = __________________
Answer:
Difference between 3\(\frac{60}{100}\) and 1\(\frac{20}{100}\), we get \(\frac{12}{5}\)
Explanation:
Difference:
3\(\frac{60}{100}\) – 1\(\frac{20}{100}\) = {[(3 × 100) + 60] ÷ 100} – {[(1 × 100) + 20] ÷ 100}
= [(300 + 60) ÷ 100] – [(100 + 20) ÷ 100]
= \(\frac{360}{100}\) – \(\frac{120}{100}\)
= (360 – 120) ÷ 100
= \(\frac{240}{100}\)
Simplest form:
\(\frac{240}{100}\) = \(\frac{240}{100}\) ÷ \(\frac{10}{10}\) = \(\frac{24}{10}\) ÷ \(\frac{2}{2}\) = \(\frac{12}{5}\)
Problem Solving
Solve. Write in simplest form.
Question 12.
Isabella has 2\(\frac{1}{4}\) oranges. Colleen has 3\(\frac{1}{4}\) oranges. How many oranges do they have altogether?
Answer:
Total number of oranges they have altogether = \(\frac{22}{4}\) or 5\(\frac{2}{4}\)
Explanation:
Number of oranges Isabella has = 2\(\frac{1}{4}\).
Number of oranges Colleen has = 3\(\frac{1}{4}\).
Total number of oranges they have altogether = Number of oranges Isabella has + Number of oranges Colleen has
= 2\(\frac{1}{4}\) + 3\(\frac{1}{4}\)
= {[(2 ×4) + 1] ÷ 4} + {[(3 ×4) + 1] ÷ 4}
= [(8 + 1) ÷ 4] + [(12 + 1) ÷ 4]
= \(\frac{9}{4}\) + \(\frac{13}{4}\)
= [(9 + 13) ÷ 4]
= \(\frac{22}{4}\) or 5\(\frac{2}{4}\)
Question 13.
Liam had 5\(\frac{7}{8}\) cups of flour. He used 2\(\frac{3}{8}\) cups of flour to make bread. How much flour does Liam have left?
Answer:
Number of cups of flour Liam had left = \(\frac{28}{8}\) or 3\(\frac{4}{8}\)
Explanation:
Number of cups of flour Liam had = 5\(\frac{7}{8}\).
Number of cups of flour he used to make bread = 2\(\frac{3}{8}\).
Number of cups of flour Liam had left = Number of cups of flour Liam had – Number of cups of flour he used to make bread
= 5\(\frac{7}{8}\) – 2\(\frac{3}{8}\)
= {[(5 ×8) + 7] ÷ 8} – {[(2 ×8) + 3] ÷ 8}
= [(40 + 7) ÷ 8] – [(16 + 3) ÷ 8]
= \(\frac{47}{8}\) – \(\frac{19}{8}\)
= (47 – 19) ÷ 8
= \(\frac{28}{8}\) or 3\(\frac{4}{8}\)
Question 14.
Audrey ran 2\(\frac{1}{6}\) miles yesterday. Today, she ran 1\(\frac{3}{6}\) miles. How many miles did she run altogether?
Answer:
Number of miles Audrey ran altogether = \(\frac{22}{6}\) or 3\(\frac{3}{6}\)
Explanation:
Number of miles Audrey ran yesterday = 2\(\frac{1}{6}\).
Number of miles Audrey ran Today = 1\(\frac{3}{6}\).
Number of miles Audrey ran altogether = Number of miles Audrey ran yesterday + Number of miles Audrey ran Today
= 2\(\frac{1}{6}\) + 1\(\frac{3}{6}\)
= {[(2 × 6) + 1] ÷ 6} + {[(1 ×6) + 3] ÷ 6}
= [(12 + 1) ÷ 6] + [(6 + 3) ÷ 6]
= \(\frac{13}{6}\) + \(\frac{9}{6}\)
= (13 + 9) ÷ 6
= \(\frac{22}{6}\) or 3\(\frac{3}{6}\)
Test Practice
Question 15.
Isaac’s paper airplane flew 5\(\frac{2}{12}\) feet. Lillian’s paper airplane flew 5\(\frac{5}{12}\) feet. How much farther did Lillian’s paper airplane fly?
(A) \(\frac{1}{4}\) feet
(B) \(\frac{3}{5}\) feet
(C) 5\(\frac{1}{12}\) feet
(D) 5\(\frac{7}{12}\) feet
Answer:
Number of feet Lillian’s paper airplane fly = \(\frac{1}{4}\)
(A) \(\frac{1}{4}\) feet
Explanation:
Number of feet Isaac’s paper airplane flew = 5\(\frac{2}{12}\).
Number of feet Lillian’s paper airplane flew = 5\(\frac{5}{12}\).
Number of feet Lillian’s paper airplane fly = Number of feet Lillian’s paper airplane flew – Number of feet Isaac’s paper airplane flew
= 5\(\frac{5}{12}\) – 5\(\frac{2}{12}\)
= {[(5 × 12) + 5] ÷ 12} – {[(5 × 12) + 2] ÷ 12}
= [(60 + 5) ÷ 12] – [(60 + 2) ÷ 12]
= \(\frac{65}{12}\) – \(\frac{62}{12}\)
= (65 – 62) ÷ 12
= \(\frac{3}{12}\) ÷ \(\frac{3}{3}\)
= \(\frac{1}{4}\)