Exercise 45 Page 36

We are asked to select all the equations that are true. & 14 ÷ 7/10=14 * 10/7 [1em] & 10 ÷ 3/5=10 * 5/3 [1em] & 16 ÷ 4/5=1/16 * 4/5 [1em] & 12 ÷ 2/3=1/12 * 2/3 [1em] & 20 ÷ 4=20 * 1/4 [1em] We will analyze the equations one at at a time. Let's start with the first equation.

First Equation

In the first option, we are given the following equation. 14 ÷ 7/10=14 * 10/7 Recall that to divide by a fraction, we can multiply by its reciprocal. 14 ÷ 7/10=14 * 10/7 ⇕ 14 * 10/7=14 * 10/7 ✓ As we can see, the left- and right-hand sides of the equation are equal. This means that the equation is true! ✓ 14 ÷ 7/10=14 * 10/7

Second Equation

Let's take a look at the second equation. 10 ÷ 3/5=10 * 5/3 We can simplify the left-hand side of the equation by multiplying by the reciprocal of the fraction. 10 ÷ 3/5=10 * 5/3 ⇕ 10 * 5/3=10 * 5/3 ✓ We can see that both sides of this equation are the same. This equation is also true! &✓ 14 ÷ 7/10=14 * 10/7 [1em] &✓ 10 ÷ 3/5=10 * 5/3

Third Equation

Next, we will determine if the following equation is true. 16÷ 4/5=1/16*4/5 Let's simplify the left-hand side of the equation! Instead of dividing by a fraction, we will multiply by its reciprocal. 16 ÷ 4/5=1/16*4/5 ⇕ 16 * 5/4=1/16*4/5 Notice that the left- and right-hand sides of the equation are not the same. Because of this, we do not know if the equation is true or false yet. We need to simplify further! We found that the third equation is false! &✓ 14 ÷ 7/10=14 * 10/7 [1em] &✓ 10 ÷ 3/5=10 * 5/3 [1em] &* 16 ÷ 4/5=1/16* 4/5

Fourth Equation

In the fourth option, we are given the following equation. 12÷ 2/3=1/12*2/3 Let's simplify the left-hand side of the equation! 12 ÷ 2/3=1/12*2/3 ⇕ 12 * 3/2=1/12*2/3 Now, we will multiply the fractions to simplify it further. We got a false statement, so we know that the fourth equation is not true. &✓ 14 ÷ 7/10=14 * 10/7 [1em] &✓ 10 ÷ 3/5=10 * 5/3 [1em] &* 16 ÷ 4/5=1/16* 4/5 [1em] &* 12 ÷ 2/3=1/12* 2/3

Fifth Equation

Let's take a look at the last equation. 20÷ 4=20*1/4 Let's write the left-hand side as a fraction. 20÷ 4=20*1/4 ⇕ 20/4=20*1/4 Now let's simplify the right-hand side. To multiply a whole number by a fraction, we need to first write the whole number as a fraction. We got a true statement! This means that the last equation is true. &✓ 14 ÷ 7/10=14 * 10/7 [1em] &✓ 10 ÷ 3/5=10 * 5/3 [1em] &* 16 ÷ 4/5=1/16* 4/5 [1em] &* 12 ÷ 2/3=1/12* 2/3 [1em] &✓ 20 ÷ 4=20* 1/4 We have selected all the equations that are true.