Simplify Fractions worksheet

1. Are they equivalent? Not equivalent

1. To test two fractions, cross-multiply: each top number times the other fraction's bottom number. They're equal exactly when both answers match

   $\frac{18}{26}\text{≟}\frac{18}{15}$

2. Multiply the first top number by the second bottom number

   $18\times 15$$=270$

3. Multiply the first bottom number by the second top number

   $26\times 18$$=468$

4. The cross products differ, so the fractions are not equivalent

   $270\text{≠}468\to \text{Not equivalent}$

5. Double-check by simplifying both fractions to lowest terms

   $\frac{18}{26}=\frac{9}{13},\frac{18}{15}=\frac{6}{5}$

2. Simplified fraction: 9/10

1. Find the biggest number that divides both the top and bottom evenly, called the GCD. Divide, keep what's left over, and repeat until nothing is left

   $\text{GCD(18, 20)}$

2. 20 ÷ 18 leaves 2 left over

   $20$$=1\times 18+2$

3. Nothing is left over, so the last number you divided by, 2, is the GCD

   $18$$=9\times 2+0$

4. Divide the top and bottom by the GCD, 2, to get the simplest form

   $\frac{18÷2}{20÷2}$$=\frac{9}{10}$

3. Simplified fraction: 9/11

1. Find the biggest number that divides both the top and bottom evenly, called the GCD. Divide, keep what's left over, and repeat until nothing is left

   $\text{GCD(18, 22)}$

2. 22 ÷ 18 leaves 4 left over

   $22$$=1\times 18+4$

3. 18 ÷ 4 leaves 2 left over

   $18$$=4\times 4+2$

4. Nothing is left over, so the last number you divided by, 2, is the GCD

   $4$$=2\times 2+0$

5. Divide the top and bottom by the GCD, 2, to get the simplest form

   $\frac{18÷2}{22÷2}$$=\frac{9}{11}$

4. Are they equivalent? Not equivalent

1. To test two fractions, cross-multiply: each top number times the other fraction's bottom number. They're equal exactly when both answers match

   $\frac{16}{18}\text{≟}\frac{12}{22}$

2. Multiply the first top number by the second bottom number

   $16\times 22$$=352$

3. Multiply the first bottom number by the second top number

   $18\times 12$$=216$

4. The cross products differ, so the fractions are not equivalent

   $352\text{≠}216\to \text{Not equivalent}$

5. Double-check by simplifying both fractions to lowest terms

   $\frac{16}{18}=\frac{8}{9},\frac{12}{22}=\frac{6}{11}$

5. Are they equivalent? Not equivalent

1. To test two fractions, cross-multiply: each top number times the other fraction's bottom number. They're equal exactly when both answers match

   $\frac{18}{34}\text{≟}\frac{13}{22}$

2. Multiply the first top number by the second bottom number

   $18\times 22$$=396$

3. Multiply the first bottom number by the second top number

   $34\times 13$$=442$

4. The cross products differ, so the fractions are not equivalent

   $396\text{≠}442\to \text{Not equivalent}$

5. Double-check by simplifying both fractions to lowest terms

   $\frac{18}{34}=\frac{9}{17},\frac{13}{22}=\frac{13}{22}$

6. Are they equivalent? Not equivalent

1. To test two fractions, cross-multiply: each top number times the other fraction's bottom number. They're equal exactly when both answers match

   $\frac{20}{24}\text{≟}\frac{14}{20}$

2. Multiply the first top number by the second bottom number

   $20\times 20$$=400$

3. Multiply the first bottom number by the second top number

   $24\times 14$$=336$

4. The cross products differ, so the fractions are not equivalent

   $400\text{≠}336\to \text{Not equivalent}$

5. Double-check by simplifying both fractions to lowest terms

   $\frac{20}{24}=\frac{5}{6},\frac{14}{20}=\frac{7}{10}$

7. Simplified fraction: 6/11

1. Find the biggest number that divides both the top and bottom evenly, called the GCD. Divide, keep what's left over, and repeat until nothing is left

   $\text{GCD(12, 22)}$

2. 22 ÷ 12 leaves 10 left over

   $22$$=1\times 12+10$

3. 12 ÷ 10 leaves 2 left over

   $12$$=1\times 10+2$

4. Nothing is left over, so the last number you divided by, 2, is the GCD

   $10$$=5\times 2+0$

5. Divide the top and bottom by the GCD, 2, to get the simplest form

   $\frac{12÷2}{22÷2}$$=\frac{6}{11}$

8. Simplified fraction: 11/10

1. Find the biggest number that divides both the top and bottom evenly, called the GCD. Divide, keep what's left over, and repeat until nothing is left

   $\text{GCD(22, 20)}$

2. 22 ÷ 20 leaves 2 left over

   $22$$=1\times 20+2$

3. Nothing is left over, so the last number you divided by, 2, is the GCD

   $20$$=10\times 2+0$

4. Divide the top and bottom by the GCD, 2, to get the simplest form

   $\frac{22÷2}{20÷2}$$=\frac{11}{10}$

9. Are they equivalent? Not equivalent

1. To test two fractions, cross-multiply: each top number times the other fraction's bottom number. They're equal exactly when both answers match

   $\frac{21}{28}\text{≟}\frac{10}{22}$

2. Multiply the first top number by the second bottom number

   $21\times 22$$=462$

3. Multiply the first bottom number by the second top number

   $28\times 10$$=280$

4. The cross products differ, so the fractions are not equivalent

   $462\text{≠}280\to \text{Not equivalent}$

5. Double-check by simplifying both fractions to lowest terms

   $\frac{21}{28}=\frac{3}{4},\frac{10}{22}=\frac{5}{11}$

10. Are they equivalent? Not equivalent

1. To test two fractions, cross-multiply: each top number times the other fraction's bottom number. They're equal exactly when both answers match

   $\frac{23}{20}\text{≟}\frac{18}{16}$

2. Multiply the first top number by the second bottom number

   $23\times 16$$=368$

3. Multiply the first bottom number by the second top number

   $20\times 18$$=360$

4. The cross products differ, so the fractions are not equivalent

   $368\text{≠}360\to \text{Not equivalent}$

5. Double-check by simplifying both fractions to lowest terms

   $\frac{23}{20}=\frac{23}{20},\frac{18}{16}=\frac{9}{8}$