Learn on PengienVision, Mathematics, Grade 5Chapter 8: Apply Understanding of Multiplication to Multiply Fractions

Lesson 5: Multiply Two Fractions

In this Grade 5 lesson from enVision Mathematics Chapter 8, students learn how to multiply two fractions by multiplying numerators together and denominators together, then simplifying to find equivalent fractions. The lesson builds on students' understanding of fractions as parts of a whole, using real-world contexts like finding a fractional part of a fractional quantity. Students practice the procedure across a range of problems, including expressions that combine addition or subtraction with multiplication of fractions.

Section 1

Multiply Fractions

Property

If aa, bb, cc, and dd are numbers where b≠0b \neq 0 and d≠0d \neq 0, then

ab⋅cd=acbd\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}

To multiply fractions, we multiply the numerators and multiply the denominators. Then we write the fraction in simplified form.

Examples

  • To multiply 23⋅45\frac{2}{3} \cdot \frac{4}{5}, multiply the numerators (2⋅4=82 \cdot 4 = 8) and the denominators (3⋅5=153 \cdot 5 = 15). The result is 815\frac{8}{15}.
  • Multiply −47⋅1416-\frac{4}{7} \cdot \frac{14}{16}. The product will be negative. We can simplify before multiplying: −47⋅2⋅74⋅4=−11⋅24=−24-\frac{4}{7} \cdot \frac{2 \cdot 7}{4 \cdot 4} = -\frac{1}{1} \cdot \frac{2}{4} = -\frac{2}{4}, which simplifies to −12-\frac{1}{2}.
  • To multiply 8⋅348 \cdot \frac{3}{4}, first write 8 as 81\frac{8}{1}. Then multiply: 81⋅34=244\frac{8}{1} \cdot \frac{3}{4} = \frac{24}{4}. Simplifying this fraction gives 6.

Explanation

Multiplying fractions is straightforward: multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator. Remember to simplify the resulting fraction by canceling any common factors for the final answer.

Section 2

Order of Operations with Fractions

Property

When an expression contains parentheses, perform the operation inside the parentheses first. For fractions, this means you add or subtract the fractions within the parentheses before multiplying.

(ab+cb)×de=a+cb×de (\frac{a}{b} + \frac{c}{b}) \times \frac{d}{e} = \frac{a+c}{b} \times \frac{d}{e}

Examples

  • (12+12)×38=1×38=38(\frac{1}{2} + \frac{1}{2}) \times \frac{3}{8} = 1 \times \frac{3}{8} = \frac{3}{8}
  • (56−16)×12=46×12=412=13(\frac{5}{6} - \frac{1}{6}) \times \frac{1}{2} = \frac{4}{6} \times \frac{1}{2} = \frac{4}{12} = \frac{1}{3}
  • (13+14)×25=(412+312)×25=712×25=1460=730(\frac{1}{3} + \frac{1}{4}) \times \frac{2}{5} = (\frac{4}{12} + \frac{3}{12}) \times \frac{2}{5} = \frac{7}{12} \times \frac{2}{5} = \frac{14}{60} = \frac{7}{30}

Explanation

The order of operations (PEMDAS/BODMAS) also applies to fractions. This means you must solve any calculations inside parentheses before performing other operations like multiplication. First, find a common denominator if needed and perform the addition or subtraction within the parentheses. Then, multiply the resulting fraction by the fraction outside the parentheses to find the final answer.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Multiply Fractions

Property

If aa, bb, cc, and dd are numbers where b≠0b \neq 0 and d≠0d \neq 0, then

ab⋅cd=acbd\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}

To multiply fractions, we multiply the numerators and multiply the denominators. Then we write the fraction in simplified form.

Examples

  • To multiply 23⋅45\frac{2}{3} \cdot \frac{4}{5}, multiply the numerators (2⋅4=82 \cdot 4 = 8) and the denominators (3⋅5=153 \cdot 5 = 15). The result is 815\frac{8}{15}.
  • Multiply −47⋅1416-\frac{4}{7} \cdot \frac{14}{16}. The product will be negative. We can simplify before multiplying: −47⋅2⋅74⋅4=−11⋅24=−24-\frac{4}{7} \cdot \frac{2 \cdot 7}{4 \cdot 4} = -\frac{1}{1} \cdot \frac{2}{4} = -\frac{2}{4}, which simplifies to −12-\frac{1}{2}.
  • To multiply 8⋅348 \cdot \frac{3}{4}, first write 8 as 81\frac{8}{1}. Then multiply: 81⋅34=244\frac{8}{1} \cdot \frac{3}{4} = \frac{24}{4}. Simplifying this fraction gives 6.

Explanation

Multiplying fractions is straightforward: multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator. Remember to simplify the resulting fraction by canceling any common factors for the final answer.

Section 2

Order of Operations with Fractions

Property

When an expression contains parentheses, perform the operation inside the parentheses first. For fractions, this means you add or subtract the fractions within the parentheses before multiplying.

(ab+cb)×de=a+cb×de (\frac{a}{b} + \frac{c}{b}) \times \frac{d}{e} = \frac{a+c}{b} \times \frac{d}{e}

Examples

  • (12+12)×38=1×38=38(\frac{1}{2} + \frac{1}{2}) \times \frac{3}{8} = 1 \times \frac{3}{8} = \frac{3}{8}
  • (56−16)×12=46×12=412=13(\frac{5}{6} - \frac{1}{6}) \times \frac{1}{2} = \frac{4}{6} \times \frac{1}{2} = \frac{4}{12} = \frac{1}{3}
  • (13+14)×25=(412+312)×25=712×25=1460=730(\frac{1}{3} + \frac{1}{4}) \times \frac{2}{5} = (\frac{4}{12} + \frac{3}{12}) \times \frac{2}{5} = \frac{7}{12} \times \frac{2}{5} = \frac{14}{60} = \frac{7}{30}

Explanation

The order of operations (PEMDAS/BODMAS) also applies to fractions. This means you must solve any calculations inside parentheses before performing other operations like multiplication. First, find a common denominator if needed and perform the addition or subtraction within the parentheses. Then, multiply the resulting fraction by the fraction outside the parentheses to find the final answer.