how can you do this

Question

I am studying for a math test and I need to figure out what 3  1/2 divided by 3/4s with a model and number line . I also need to figure out what 3/4 divided by 1/12 is . using a number line and model . con you help please respond asap

Answer 1

When you divide by fractions, you are essentially multiplying by the fraction's inverse, so what happens when you divide by 3/4, you will be multiplying by 4/3, and when you divide by 1/12, you will be multiply by 12

 

3 * 2 + 1 = 7

so we have ⁷/₂ * ⁴/₃ = ²⁸/₆ → ¹⁴/₃, or 4 ²/₃ converted.

 

³/₄ * 12 = ³⁶/₄ → 9

 

A number line is easy, but tricky if you aren't paying attention to what the numbers are doing.  What you are doing is you are starting at 0 and counting up by fractions until we reach the designated number.  In other words, we start at 0, and jump 3/4 of a number until we reach  3 ¹/₂.

 

0-----.5--X₁--1-----1.5(X₂)-----2--X₃---2.5-----3(X₄)-----3.5--X₅---4-----4.5-----5

As you can see, the 5^th jump is too far, but it is at the right place to be ²/₃ from the previous jump and ¹/₃ away from the completed 5^th jump.

 

The second number line works the same sort of way, only you will be moving by 1/12th increments with each jump until you reach ³/₄.