Equivalent Fractions

Show your work for each problem.

1.
Which fraction is equivalent to $\frac{1}{2}$ ?
1. a) $\frac{1}{4}$
2. b) $\frac{3}{4}$
3. c) $\frac{2}{4}$
4. d) $\frac{2}{3}$
Answer: $\frac{2}{4}$
$\frac{1}{2} \times \frac{2}{2} = \frac{2}{4}$ . Both fractions represent the same value: half.
2.
Which fraction is NOT equivalent to $\frac{3}{4}$ ?
1. a) $\frac{9}{12}$
2. b) $\frac{4}{5}$
3. c) $\frac{6}{8}$
4. d) $\frac{12}{16}$
Answer: $\frac{4}{5}$
$\frac{4}{5}$ equals 0.8, while $\frac{3}{4}$ equals 0.75. The other fractions all simplify to $\frac{3}{4}$ .
3.
Complete: $\frac{2}{5} = \frac{?}{10}$
Answer: 4
Since $5 \times 2 = 10$ , we multiply the numerator by 2 as well: $2 \times 2 = 4$ . So $\frac{2}{5} = \frac{4}{10}$ .
4.
Simplify $\frac{4}{8}$ to lowest terms. Write only the numerator.
Answer: 1
The GCF of 4 and 8 is 4. $\frac{4 \div 4}{8 \div 4} = \frac{1}{2}$ . The numerator is 1.
5.
Look at $\frac{2}{6}$ and $\frac{1}{3}$ . Which statement is true?
1. a) $\frac{1}{3}$ is greater, because its pieces are bigger
2. b) $\frac{2}{6}$ is greater, because its numbers are bigger
3. c)They are equivalent: $\frac{2}{6} = \frac{1}{3}$
4. d)They cannot be compared, because the denominators are different
Answer: They are equivalent: $\frac{2}{6} = \frac{1}{3}$
$\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}$ . They are equivalent: bigger numbers do not mean a bigger fraction, and fractions with different denominators can still be compared.
6.
Which fraction is equivalent to $\frac{5}{8}$ ?
1. a) $\frac{10}{24}$
2. b) $\frac{8}{11}$
3. c) $\frac{15}{24}$
4. d) $\frac{15}{8}$
Answer: $\frac{15}{24}$
$\frac{5}{8} \times \frac{3}{3} = \frac{15}{24}$ . The others are common mistakes: $\frac{8}{11}$ adds 3 to the top and bottom, $\frac{15}{8}$ multiplies only the numerator, and $\frac{10}{24}$ multiplies the numerator and denominator by different numbers.
7.
Complete: $\frac{?}{15} = \frac{2}{3}$
Answer: 10
$3 \times 5 = 15$ , so $2 \times 5 = 10$ . Therefore $\frac{10}{15} = \frac{2}{3}$ .
8.
Simplify $\frac{12}{18}$ to lowest terms. What is the denominator of the simplified fraction?
Answer: 3
GCF of 12 and 18 is 6. $\frac{12 \div 6}{18 \div 6} = \frac{2}{3}$ . The denominator is 3.
9.
Emma ate $\frac{3}{6}$ of a cake and Leo ate $\frac{2}{4}$ of an identical cake. Who ate more?
1. a)They ate the same amount
2. b)Cannot be determined
3. c)Leo ate more
4. d)Emma ate more
Answer: They ate the same amount
$\frac{3}{6} = \frac{1}{2}$ and $\frac{2}{4} = \frac{1}{2}$ . Both ate exactly half!
10.
If $\frac{4}{7} = \frac{x}{21}$ , what is $x$ ?
Answer: 12
$7 \times 3 = 21$ , so we multiply the numerator by 3: $4 \times 3 = 12$ . Therefore $x = 12$ .
11.
Find three fractions equivalent to $\frac{3}{5}$ .
Answer: 6/10, 9/15, 12/20
1. Multiply the numerator and denominator by 2: $\frac{3}{5} = \frac{\square}{10}$ . What goes in the box? 6
2. Multiply the numerator and denominator by 3: $\frac{3}{5} = \frac{\square}{15}$ . What goes in the box? 9
3. Multiply the numerator and denominator by 4: $\frac{3}{5} = \frac{\square}{20}$ . What goes in the box? 12
12.
Simplify $\frac{24}{36}$ step by step to lowest terms.
Answer: 2/3
1. Find the greatest common factor (GCF) of 24 and 36. 12
2. Divide the numerator by the GCF: $24 \div 12 = ?$ 2
3. Divide the denominator by the GCF: $36 \div 12 = ?$ 3
4. Can $\frac{2}{3}$ be simplified any further? no
13.
Use cross multiplication to check if $\frac{5}{8}$ and $\frac{15}{24}$ are equivalent.
Answer: Yes, they are equivalent
1. Multiply the first numerator by the second denominator: $5 \times 24 = ?$ 120
2. Multiply the first denominator by the second numerator: $8 \times 15 = ?$ 120
3. Are the cross products equal? yes
4. So are the fractions equivalent? yes
14.
Find the value of $x$ if $\frac{x}{35} = \frac{3}{7}$ .
Answer: 15
$7 \times 5 = 35$ , so $3 \times 5 = 15$ . Therefore $x = 15$ and $\frac{15}{35} = \frac{3}{7}$ .
15.
Recipe A uses $\frac{2}{3}$ cup of flour and Recipe B uses $\frac{5}{8}$ cup. Which recipe uses more flour? Rewrite both fractions with the denominator 24 to compare them.
Answer: Recipe A: 2/3 = 16/24 > 15/24 = 5/8
1. What do you multiply 3 by to get 24? 8
2. Recipe A: $\frac{2}{3} = \frac{\square}{24}$ . What goes in the box? 16
3. Recipe B: $8 \times 3 = 24$ , so $\frac{5}{8} = \frac{\square}{24}$ . What goes in the box? 15
4. Which fraction is larger? 2/3
16.
Which pair of fractions is NOT equivalent?
1. a) $\frac{4}{6}$ and $\frac{8}{10}$
2. b) $\frac{3}{9}$ and $\frac{1}{3}$
3. c) $\frac{8}{12}$ and $\frac{2}{3}$
4. d) $\frac{5}{15}$ and $\frac{2}{6}$
Answer: $\frac{4}{6}$ and $\frac{8}{10}$
$\frac{4}{6} = \frac{2}{3}$ but $\frac{8}{10} = \frac{4}{5}$ . These are different values! The other pairs all simplify to the same fraction.
17.
Find the missing values: $\frac{3}{4} = \frac{a}{20} = \frac{21}{b}$
Answer: a = 15, b = 28
1. For $\frac{3}{4} = \frac{a}{20}$ : What is $4 \times ? = 20$ ? 5
2. So $a = 3 \times 5 = ?$ 15
3. For $\frac{3}{4} = \frac{21}{b}$ : What is $3 \times ? = 21$ ? 7
4. So $b = 4 \times 7 = ?$ 28
18.
Tom has $\frac{8}{12}$ of a chocolate bar. Maria has $\frac{10}{15}$ of an identical bar. Do they have the same amount? Prove it.
Answer: Yes, they have the same amount
1. Simplify Tom's fraction by dividing by 4: $\frac{8}{12} = \frac{\square}{3}$ . What goes in the box? 2
2. Simplify Maria's fraction by dividing by 5: $\frac{10}{15} = \frac{\square}{3}$ . What goes in the box? 2
3. Are the simplified fractions equal? yes
4. So do Tom and Maria have the same amount? yes