Year 7 Fractions: Multiplying, Dividing, and Word Problems

Mastering Math Fractions in Year 7: Multiplying, Dividing, and Solving Word Problems

In Year 7, students are introduced to more complex mathematical concepts, including fractions. This article will explore two essential subtopics within fractions: multiplying and dividing fractions, as well as solving fraction word problems.

1. Multiplying Fractions

Multiplying fractions involves finding the product of two or more fractions. To do this, you multiply the numerators together and the denominators together:

(a/b) * (c/d) = (a * c) / (b * d)

For example:

0.3 * 0.5 = (3/10) * (5/1) = 15/10 = 1.5

Practice Problem:

Multiply 2/3 * 4/5

Answer: (2 * 4) / (3 * 5) = 8/15

2. Dividing Fractions

Dividing fractions involves finding the quotient of two fractions. This is achieved by multiplying the first fraction by the reciprocal of the second fraction:

(a/b) ÷ (c/d) = (a/b) * (d/c)

For example:

0.5 ÷ 0.2 = (5/10) * (10/2) = 25/2 = 12.5

Practice Problem:

Divide 3/4 by 2/3

Answer: (3/4) * (3/2) = (3 * 3) / (4 * 2) = 9/8

3. Solving Fraction Word Problems

Word problems can be tricky, but they help students apply their fraction knowledge to real-world scenarios. We'll look at two common types of word problems:

• Fraction Comparison: Determine which fraction is larger or smaller.

Example: A bag contains 2/3 apples and 1/4 oranges. Which fruit makes up a larger fraction of the bag's contents?

Answer: 2/3 apples make up a larger fraction of the bag's contents.

• Fraction Arithmetic: Apply operations (such as addition, subtraction, multiplication, or division) to fractions to find the final result.

Example: In a box, there are 4/5 toys that are red, and 1/3 toys are blue. How many toys in the box are neither red nor blue?

Answer: First, find the fraction of toys that are either red or blue: 4/5 (red) + 1/3 (blue) = (4 * 3) / (5 * 3) = 12/15 = 4/5

Now, subtract this fraction from 1 to find the fraction of toys that are neither red nor blue:

1 - 4/5 = (5 - 4) / 5 = 1/5

So, 1/5 of the toys in the box are neither red nor blue.

These are a few examples of how multiplication and division with fractions can be applied to solve word problems. The key to success is understanding how to manipulate fractions and consistently follow the rules for each operation. Practice is essential to build confidence and fluency with these skills.