Page 2: Simplifying Ratios

This page focuses on the process of simplifying ratios and provides various examples and practice problems.

Simplifying ratios involves finding the greatest common factor (GCF) and dividing both parts of the ratio by it. The page offers tips for identifying divisibility:

Vocabulary: Divisibility rules

• If a number ends in 0 or 5, it's divisible by 5
• If a number is even, it's divisible by 2

The page presents multiple examples of simplifying ratios, including:

• 6:9 simplified to 2:3
• 15 min : 35 min simplified to 3:7
• 32 cm : 26 cm simplified to 16:13

Example: Simplify 35:60

1. Find the GCF: 5
2. Divide both parts by 5: 35 ÷ 5 = 7, 60 ÷ 5 = 12
3. Simplified ratio: 7:12

The page also includes practice problems for students to apply the simplification process to various ratios.

Page 3: Expressing Ratios in the Form 1:n and n:1

This page explains how to express ratios in the form 1:n and n:1, which is useful for comparing ratios and solving real-world problems.

The process for expressing ratios in the form 1:n involves:

1. Set up the answer with the ratio above 1:n
2. Divide the ratio by the number within the ratio that has the '1' on its side
3. State the new ratio (1:n or n:1)

Definition: 1:n form - A ratio expressed with 1 as the first term and n as a decimal or whole number.

The page provides several examples and practice problems for expressing ratios in both 1:n and n:1 forms.

Example: Express 2:3 in the form 1:n

1. Set up: 2:3 / 2:3
2. Divide: 2 ÷ 2 = 1, 3 ÷ 2 = 1.5
3. Result: 1:1.5

Students are encouraged to practice with various ratios, including those involving decimals and fractions.

Page 4: Additional Practice Problems

The final page offers additional practice problems for expressing ratios in the forms 1:n and n:1. These exercises reinforce the concepts learned in the previous pages and provide students with more opportunities to apply their skills.

Highlight: Practicing with a variety of ratio problems helps students develop confidence and proficiency in working with ratios in different forms.

The page includes ratios such as:

• 19:20 to be expressed as n:1
• 207:50 to be expressed as n:1
• 38:55 to be expressed as 1:n

By working through these problems, students can solidify their understanding of ratio manipulation and prepare for more complex applications in real-world scenarios.

Example: Express 207:50 as n:1

1. Divide 207 by 50: 207 ÷ 50 = 4.14
2. Result: 4.14:1

This comprehensive guide on sharing money using ratios and simplifying ratios provides students with the necessary tools to tackle ratio problems confidently in their academic and everyday lives.

Page 1: Sharing Money Using Ratios

This page introduces the concept of sharing money using ratios with examples and practice problems.

The process of sharing money using ratios involves three main steps:

1. Add together the total parts in the ratio
2. Divide the given quantity by the total number of parts
3. Multiply what one part equals by the parts in the ratio

Example: Share $30 in the ratio 2:3

1. Total parts: 2 + 3 = 5
2. Value of one part: $30 ÷ 5 =$6
3. Final distribution: 2 parts = $12, 3 parts =$18

The page provides additional examples, including sharing $100 in the ratio 9:3:8 and$200 in the ratio 2:3:5.

Highlight: When sharing money in ratios, the value of one part can be a decimal.

Practice problems are included for students to apply the learned concepts, such as sharing £40 in the ratio 3:7 and £111 in the ratio 1:7.