Question

Julie usually puts \(23 \frac{1}{4}\) pounds of flour in her cookie recipe, but this time she is short of another ingredient and must cut her flour by \(7 \frac{3}{5}\) pounds. How much flour will she put in the recipe? A. \(15 \frac{13}{20}\) pounds B. \(16 \frac{1}{2}\) pounds C. \(16 \frac{4}{9}\) pounds D. \(30 \frac{4}{9}\) pounds

Short answer

The amount of flour Julie will put in the recipe is \(15 \frac{13}{20}\) pounds. This corresponds to option A.

Step-by-step solution

Convert Mixed Numbers to Improper Fractions

First, convert the mixed numbers into improper fractions. For Julie's usual amount of flour: \(23 \frac{1}{4} = 23 + \frac{1}{4} = \frac{92}{4} + \frac{1}{4} = \frac{92+1}{4} = \frac{93}{4}\). For the amount she needs to cut: \(7 \frac{3}{5} = 7 + \frac{3}{5} = \frac{35}{5} + \frac{3}{5} = \frac{35+3}{5} = \frac{38}{5}\).

Find Common Denominator

To subtract fractions, they need a common denominator. The least common multiple of 4 and 5 is 20. Convert each fraction to have a denominator of 20. For \( \frac{93}{4} \): \( \frac{93 \times 5}{4 \times 5} = \frac{465}{20} \). For \( \frac{38}{5} \): \( \frac{38 \times 4}{5 \times 4} = \frac{152}{20} \).

Subtract the Fractions

Subtract the improper fractions: \( \frac{465}{20} - \frac{152}{20} = \frac{465 - 152}{20} = \frac{313}{20} \).

Convert Improper Fraction Back to Mixed Number

Convert the resulting improper fraction back to a mixed number. \( \frac{313}{20} = 15 \frac{13}{20} \) because 313 divided by 20 is 15 with a remainder of 13.

Key concepts

Fractions

Fractions are a way to represent parts of a whole. A fraction is made up of two numbers separated by a slash. The number above the slash is called the numerator, and it tells you how many parts you have. The number below the slash is called the denominator, and it tells you how many parts make up a whole. For example, in the fraction \(\frac{1}{4}\), 1 is the numerator and 4 is the denominator. This means you have 1 part of something that is divided into 4 equal parts. Fractions are essential in many areas like cooking, measurements, and even in grade school math.

Mixed Numbers

A mixed number combines a whole number with a fraction. An example is \(\text{23}\frac{1}{4}\), which means 23 whole parts and a quarter of a part. Mixed numbers are commonly used in everyday situations where you have more than a whole but less than the next whole number. To work with mixed numbers in calculations, it's often easier to first convert them into improper fractions.

Subtraction of Fractions

Subtracting fractions involves a few steps. First, make sure the fractions have the same denominator. This is often called finding a common denominator. For example, if you're subtracting \(\frac{3}{5}\) from \(\frac{6}{7}\), you would need to convert these fractions so that they have the same denominator. After that, simply subtract the numerators and place the result over the common denominator. Finally, if necessary, simplify the fraction. If you're working with mixed numbers, convert them into improper fractions before performing the subtraction, and then convert back if needed.

Improper Fractions

An improper fraction is a fraction where the numerator is larger than the denominator, for instance, \(\frac{9}{4}\). This means you have more than one whole. Improper fractions are often the result of converting mixed numbers for ease of calculation. To convert an improper fraction back into a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder is the new numerator of the fractional part. For example, \(\frac{9}{4}\) can be converted to \(\text{2}\frac{1}{4}\).