Question

1. model with math wendy uses \\(\frac{2}{12}\\) of a loaf of bread to make one sandwich. write and solve an equation to find \\(b\\), how much of the loaf of bread she uses to make 4 sandwiches. use a drawing, as needed. 12. higher order thinking a baker uses \\(\frac{2}{3}\\) cup of rye flour in each loaf of bread. how many cups of rye flour will the baker use in 3 loaves? in 7 loaves? in 10 loaves?

Explanation:

Problem 11

Step1: Define the equation

Let \( b \) be the amount of the loaf used for 4 sandwiches. Since each sandwich uses \( \frac{2}{12} \) of a loaf, for 4 sandwiches, the equation is \( b = 4\times\frac{2}{12} \).

Step2: Simplify the equation

Simplify \( 4\times\frac{2}{12} \). First, multiply the numerators: \( 4\times2 = 8 \), so we have \( \frac{8}{12} \). Then simplify the fraction by dividing numerator and denominator by 4: \( \frac{8\div4}{12\div4}=\frac{2}{3} \).

Step1: For 3 loaves

The amount of rye flour used for \( n \) loaves is \( \frac{2}{3}\times n \). For \( n = 3 \), calculate \( \frac{2}{3}\times3 \). The 3 in the numerator and denominator cancels out, so \( \frac{2\times3}{3}=2 \) cups.

Step2: For 7 loaves

Using the formula \( \frac{2}{3}\times7 \). Multiply the numerators: \( 2\times7 = 14 \), so we have \( \frac{14}{3}=4\frac{2}{3} \) cups.

Step3: For 10 loaves

Using the formula \( \frac{2}{3}\times10 \). Multiply the numerators: \( 2\times10 = 20 \), so we have \( \frac{20}{3}=6\frac{2}{3} \) cups.

Answer:

The equation is \( b = 4\times\frac{2}{12} \) and \( b=\frac{2}{3} \) of the loaf.

Problem 12