Compare fractions: word problems

Learning Objectives Identify fractions and quantities to be compared within word problems. Determine appropriate strategies (common denominator, cross-multiplication, converting to decimals) to compare fractions. Solve word problems involving the comparison of two or more fractions. Interpret the results of fraction comparisons in the context of the word problem. Justify fraction comparisons using mathematical reasoning. Convert between mixed numbers and improper fractions when necessary for comparison. Ever wonder who ate more pizza 🍕 or which recipe calls for less sugar? Comparing fractions helps us answer these everyday questions! In this lesson, you'll learn how to tackle word problems that require comparing fractions. We'll explore different strategies to de...

TermDefinitionExample FractionA number representing a part of a whole, expressed as a numerator over a denominator.In the fraction 3/4, 3 is the part and 4 is the whole. NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In 5/8, the numerator is 5. DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In 5/8, the denominator is 8. Equivalent FractionsFractions that represent the same value, even though they have different numerators and denominators.1/2, 2/4, and 3/6 are all equivalent fractions. Common DenominatorA shared denominator for two or more fractions, which is necessary to add, subtract, or easily compare them.For 1/3 and 1/4, a common denominator is 12. Least Common Multip...

Comparing Fractions with a Common Denominator If $\frac{a}{c}$ and $\frac{b}{c}$ are two fractions with the same positive denominator $c$, then $\frac{a}{c} > \frac{b}{c}$ if $a > b$, and $\frac{a}{c} < \frac{b}{c}$ if $a < b$. To compare fractions, first find a common denominator. Once the denominators are the same, compare the numerators directly. The fraction with the larger numerator is the greater fraction. Comparing Fractions using Cross-Multiplication To compare $\frac{a}{b}$ and $\frac{c}{d}$, calculate the cross-products $a \times d$ and $b \times c$. If $a \times d > b \times c$, then $\frac{a}{b} > \frac{c}{d}$. If $a \times d < b \times c$, then $\frac{a}{b} < \frac{c}{d}$. This method allows you to compare fractions without finding a comm...