Multiplying Fractions with Integers and Fractions

About this resource

What's inside this resource

Multiplying two fractions and multiplying a fraction by an integer are taught in parallel strands, each opening with an array-model teaching page before moving into worksheet practice. A 14-page guide explains two solution methods (multiply-then-simplify versus cancel-then-multiply) and outlines seven worksheet sets covering array-based questions, calculating-and-simplifying practice at two difficulty levels, and word problems for each strand, plus an extra-challenge set multiplying three fractions together. The individual worksheet files each pair a set of computation or word problems with a fully worked answer page, such as showing that 1/8 x 3/4 x 3/12 simplifies to 1/128, and two additional one-page 'teaching pages' model a single worked example with an array diagram. The guide notes that the original digital version lets a randomiser button regenerate new question sets, though the PDF files here capture one fixed set of questions and answers per topic.

In the classroom

Teaching tips & learning objectives

Learning objectives

Multiply two fractions together and simplify the resulting product.
Multiply a fraction by a whole-number integer and express the result as a simplified mixed number where applicable.
Solve real-world word problems requiring multiplication of fractions or a fraction by an integer.
Multiply three fractions together as an extension of the two-fraction method.

Teaching tips

Introduce each strand with its array-model teaching page before assigning the matching worksheet sets, since the guide is built around visual arrays as the entry point.
Use Method 1 (multiply numerators and denominators, then simplify) for most students, but switch to Method 2 (simplify first, then multiply) when working with the three-fraction extra-challenge set, since the guide notes it is more efficient there.
Assign the word-problem sets (Set 3 and Set 6) only after students are comfortable with the array and calculation sets, since they require translating real-world scenarios into fraction multiplication.

Skills covered

Fraction-by-fraction multiplication - students solve problems such as 2/5 x 2/4 using array models and direct calculation, then simplify the result.
Fraction-by-integer multiplication - students solve problems such as 2/3 x 9 and convert improper-fraction results into simplified mixed numbers.
Word-problem translation - students convert real-world scenarios, such as recipe scaling or distance covered, into a fraction multiplication expression and solve it.
Multi-step fraction multiplication - students multiply three fractions together in the extra-challenge set, choosing between two solution methods.

Good to know

Questions teachers ask about this resource

What are the two methods the guide offers for multiplying fractions, and when does it recommend each?

Method 1 multiplies numerators and denominators before simplifying, giving more multiplication practice; Method 2 cancels terms before multiplying, giving more division practice, and the guide recommends Method 2 as the better option when multiplying three fractions.

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Curriculum

Standards, concepts & topics

Standards

4.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
5.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.