Question

show work in the spaces provided. calculators may not be used.

1. write three fractions that are equal to 40%
2. is the value of these expressions the same? explain.

4•6 - 4
4•(6 - 4)

1. find the value of the expression below:

63 - 21 + (3•11)

1. how many ½’s are there in 6?
2. if 6 cans of soup cost $1.50, how much will 9 cans cost?
3. solve ( 2\frac{2}{3} + 6\frac{7}{12} )
4. what are all the factors of 60? underline the factors that are composite. circle the factors that are prime numbers.
5. lina is making a trail mix for a hiking trip. she has ( 2\frac{1}{2} ) cups of peanuts, ( 3\frac{1}{4} ) cups of raisins, and ( 2\frac{3}{4} ) cups of banana chips. how many cups of trail mix can she make?

Explanation:

Question 1:

Step1: Convert 40% to fraction

40% = $\frac{40}{100}$

Step2: Simplify $\frac{40}{100}$

Divide numerator and denominator by 20: $\frac{40\div20}{100\div20}=\frac{2}{5}$

Step3: Find another equivalent fraction

Multiply numerator and denominator of $\frac{2}{5}$ by 2: $\frac{2\times2}{5\times2}=\frac{4}{10}$

Step4: Find third equivalent fraction

Multiply numerator and denominator of $\frac{2}{5}$ by 3: $\frac{2\times3}{5\times3}=\frac{6}{15}$

Step1: Calculate $4\bullet6 - 4$

First, multiply: $4\times6 = 24$, then subtract: $24 - 4 = 20$

Step2: Calculate $4\bullet(6 - 4)$

First, subtract inside the parentheses: $6 - 4 = 2$, then multiply: $4\times2 = 8$

Step3: Compare the results

20 ≠ 8, so the values are different because of the order of operations (PEMDAS: parentheses first).

Step1: Calculate the parentheses

$3\bullet11 = 33$

Step2: Perform subtraction and addition

$63 - 21 + 33 = 42 + 33 = 75$

Answer:

$\frac{2}{5}$, $\frac{4}{10}$, $\frac{6}{15}$ (answers may vary)

Question 2: