Multiplication: Multiplying two fractions together is quite simple. Given that multiplication is commutative (we can do it in any order), we simply perform the fractional operations of multiplication and division in sequence.

$\frac{2}{3} \times \frac{4}{5} = 1 \times 2 \div 3 \times 4 \div 5 = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$

Division: Since division is simply the inverse of multiplication, we can divide one fraction by another be inverting the division and multiplication operations (that is, we mulitply by the reciprocal):

$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3\times 4} = \frac{10}{12} = \frac{5}{6}.$

Addition: Adding fractions is slightly harder, because we can only add like items together. Thus, to add two fractions together, we must ensure that the denominators are equal.

$\frac{2}{3} + \frac{4}{5} = \frac{2 \times 5}{3 \times 5} + \frac{4 \times 3}{5 \times 3} = \frac{10}{15} + \frac{12}{15} = \frac{10+12}{15} = \frac{22}{15}.$ Note by Arron Kau
6 years, 9 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

I love it because I'm only in 6th grade and its really easy so is the other stuff

- 5 years, 12 months ago