Completing the Puzzle: How to Finishing Equations when Multiplying Fractions by Whole Numbers Using Models

When presented with incomplete equations, these models can be helpful for determining the missing value. In this guide, we’ll explore how to use visual models to finish equations that involve multiplying fractions by whole numbers.

Step-by-step Guide to Finishing Equations when Multiplying Fractions by Whole Numbers Using Models:

1. Identifying the Model:

First, determine which visual model is being used in the equation. This could be an array, a number line, an area model, or a set model.

2. Interpreting the Model:

Examine the model to understand the given information:

– For arrays, count the shaded parts.

– For number lines, identify the starting and ending points.

– For area models, measure the shaded area.

– For set models, count the divided parts.

3. Completing the Equation:

Using the information from the model:

– Multiply the fraction by the whole number.

– Place the product in the missing part of the equation.

4. Simplifying the Result:

If the result is an improper fraction, convert it to a mixed number for a clearer representation.

Example 1: (Array Model):

Given an array with 4 rows, each divided into 5 parts, and 3 parts shaded in each row, complete the equation: \( \_\_\_\_ \times \frac{3}{5} = \_\_\_\_ \)

Solution:

There are 4 rows, so the whole number is 4.

Multiplying: \( 4 \times \frac{3}{5} = \frac{12}{5} = 2 \frac{2}{5} \)

Completed equation: \( 4 \times \frac{3}{5} = 2 \frac{2}{5} \)

The Absolute Best Book for 5th Grade Students

2. Example 2 (Number Line):

Pre-Algebra for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

Given a number line starting at 0 and ending at 1.5 with jumps of \(\frac{1}{2}\), complete the equation: \( 3 \times \_\_\_\_ = 1.5 \)

Solution:

There are 3 jumps of size \(\frac{1}{2}\).

Completed equation: \( 3 \times \frac{1}{2} = 1.5 \)

Practice Questions:

1. Given an area model of a rectangle with a length of 6 and a width divided into 4 parts, with 3 parts shaded, complete the equation: \( 6 \times \_\_\_\_ = \_\_\_\_ \)

2. Using a set model with 5 groups, each divided into 6 parts, and 4 parts taken from each group, complete the equation: \( 5 \times \_\_\_\_ = \_\_\_\_ \)

3. Given a number line starting at 0 and ending at 2.25 with jumps of \(\frac{3}{4}\), complete the equation: \( \_\_\_\_ \times \frac{3}{4} = 2.25 \)

A Perfect Book for Grade 5 Math Word Problems!

Answers:

1. \( 6 \times \frac{3}{4} = 4.5 \)

2. \( 5 \times \frac{4}{6} = 3 \frac{1}{3} \)

3. \( 3 \times \frac{3}{4} = 2.25 \)

The Best Math Books for Elementary Students

Recommended EffortlessMath Books

For grade-level practice with fraction multiplication and other elementary topics, the Grade 4 Math for Beginners walks through visual models and computation. For grade 5 students extending into harder fraction work, the Grade 5 Math for Beginners covers fraction multiplication, division, and mixed-number arithmetic.

Frequently Asked Questions

How do you multiply fractions with whole numbers using models?

Draw one model for each group named by the whole number, shade the fraction in each, then count all the shaded parts. For 3 × 2/5, draw three bars split into fifths and shade 2 fifths in each. That is 6 shaded fifths, so the blank in 3 × 2/5 = ___ is 6/5, or 1 1/5. The picture and the rule (3 × 2 = 6, keep the 5) should match.

How do you multiply fractions with visual models?

Start by naming the model: an array, number line, area model or set model. Then read it carefully. On a number line, count the jumps and note how long each jump is; 4 jumps of 1/3 land at 4/3. In a set model, count the circled objects in each group. Write what you see as a whole number times a fraction, and the product completes the equation.

How do you multiply fractions using area models?

For a whole number times a fraction, draw a rectangle for each whole, divide each into equal parts set by the denominator, and shade the numerator in each one. For 2 × 3/4, two rectangles cut into fourths with 3 shaded in each give 6/4. Simplify to 3/2, or 1 1/2. If the equation shows the answer but not the fraction, count the shaded parts in one rectangle.

How do you multiply improper fractions using models?

An improper fraction is more than one whole, so each group needs more than one shape. For 2 × 5/4, show 5/4 as one full rectangle plus 1 shaded fourth of a second rectangle, then draw that twice. Counting gives 10 shaded fourths, which is 10/4 = 2 1/2. The finished equation reads 2 × 5/4 = 2 1/2, and the product is bigger than 2 because 5/4 is bigger than 1.

How do you multiply mixed fractions using models?

Show the mixed number as full shapes plus a partly shaded shape, then repeat it for each group. For 3 × 1 1/2, each group is one whole and one half, so three groups give 3 wholes and 3 halves. Three halves make 1 1/2, so the total is 4 1/2. Check with the rule: 1 1/2 = 3/2, and 3 × 3/2 = 9/2 = 4 1/2.

Is multiplying fractions hard?

Not usually, once you see what it means. Multiplying a whole number by a fraction is repeated addition of equal parts, so 4 × 1/3 is just 1/3 + 1/3 + 1/3 + 1/3 = 4/3. Models help because you can count the shaded pieces instead of memorizing steps. Most mistakes come from miscounting the model, so take a second look before writing the answer in the blank.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to multiply fractions
• Choose the right visual model for fraction multiplication
• How to simplify fractions
• How to convert improper fractions to mixed numbers
• How to find equivalent fractions