Key Concepts
- Solve constant speed problems
- Solving unit-price problems
- Using an equation to represent unit rate problems
Multiply fractions and whole numbers
Model: Standard multiplication of whole numbers and fractions
- Hal spent ¾ hour each day for 7 days. How much total time did he spend reading?


Multiply to find the number of fourths
7 x 3/4 = 7 x 3 x 1/4

= 21 x 1/4 = 21/4
Rewrite as a mixed fraction number
21/4 = 5 1/4
Hal spent 5 1/4 hours of reading.

- Explain how 3/4 x 7, 7 x 3/4 and 3 x 7/4 are all related?
Given that, prove
3/4 x 7 = 7 x 3/4 = 3 x 7/4
Case 1:
3/4 x 7 = 1/4 x 3 x 7
= 1/4 x 21
= 21/4
Case 2:
7 x 3/4
= 7 x 3 x 1/4
= 21 x 1/4
= 21/4
Case 3:
3 x 7/4
= 3 x 7 x 1/4
= 21 x 1/4
= 21/4
So,
3/4 x 7 = 7 x 3/4
= 3 x 7/4
= 21/4
Practice
1. 4/5 x 500
Solution:
4/5 x 500 = 2000/5
4/5 x 500=400
2. 5 x 2/3
Solution:
5 x 2/3
= 5 X 2/3
= 10/3 x 2/3
= 3 1/3
3. 9/10 x 25
Solution:
9/10 x 25 = 9 X 25/10
= 225/10
= 9/10 x 25 = 22.5 or 22
5/10 or 12
Related topics
Composite Figures – Area and Volume
A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book. To understand the dynamics of composite […]
Read More >>Special Right Triangles: Types, Formulas, with Solved Examples.
Learn all about special right triangles- their types, formulas, and examples explained in detail for a better understanding. What are the shortcut ratios for the side lengths of special right triangles 30 60 90 and 45 45 90? How are these ratios related to the Pythagorean theorem? Right Angle Triangles A triangle with a ninety-degree […]
Read More >>Ways to Simplify Algebraic Expressions
Simplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory. It is one of the earliest branches in the history of mathematics. The study of mathematical […]
Read More >>How to Solve Right Triangles?
In this article, we’ll learn about how to Solve Right Triangles. But first, learn about the Triangles. Triangles are made up of three line segments. These three segments meet to form three angles. The lengths of the sides and sizes of the angles are related to one another. If you know the size (length) of […]
Read More >>Other topics

Comments: