# 5.6 - Problems with Add, Subtract, & Multiply Fractions

The student will

a) solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers; and

b) solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction, with models.*

*On the state assessment, items measuring this objective are assessed without the use of a calculator.

### BIG IDEAS

• So that I can solve problems in real life situations that involve fractions
• So that I can follow double or halve a recipe when cooking for my family
• So that I can calculate measurements when building a structure
• So that pharmacists, chefs, architects, engineers and seamstresses can calculate precise measurements

### UNDERSTANDING THE STANDARD

• A fraction can be expressed in simplest form (simplest equivalent fraction) by dividing the numerator and denominator by their greatest common factor.
• When the numerator and denominator have no common factors other than one, then the fraction is in simplest form.
• Fractions having like denominators have the same meaning as fractions having common denominators.
• Addition and subtraction with fractions and mixed numbers can be modeled using a variety of concrete and pictorial representations.
• Estimation keeps the focus on the meaning of the numbers and operations, encourages reflective thinking, and helps build informal number sense with fractions. Students can reason with benchmarks to get an estimate without using an algorithm. Estimation can be used to check the reasonableness of an answer.
• A mixed number has two parts: a whole number and a fraction. The value of a mixed number is the sum of its two parts.
• A unit fraction is a fraction in which the numerator is one.
• Models for representing multiplication of fractions may include arrays, paper folding, repeated addition, fraction strips or rods, pattern blocks, or area models.
• Students should begin exploring multiplication with fractions by solving problems that involve a whole number and a unit fraction.
• When multiplying a whole number by a fraction such as 6 × 1/2 , the meaning is the same as with multiplication of whole numbers: six groups the size of 1/2 of the whole. • When multiplying a fraction by a whole number such as 1/2 × 6, we are trying to determine a part of the whole (e.g., one-half of six). • The inverse property of multiplication states that every number has a multiplicative inverse and the product of multiplicative inverses is 1 (e.g., 5 and 1/5 are multiplicative inverses because 5 × 1/5 = 1). The multiplicative inverse of a given number can be called the reciprocal of the number. Students at this level do not need to use the term for the properties of the operations.
• Multiplying a whole number by a unit fraction can be related to dividing the whole number by the denominator of the fraction. For example, 1/3 of 6 is equivalent to 2. This understanding forms a foundation for learning how to multiply a whole number by a proper fraction. • At this level, students will use models to solve problems that involve multiplication of a whole number, limited to 12 or less, and a proper fraction where the denominator is a factor of the whole number. For example, a model for 3/4 × 8 or 8 × 3/4 shows that the answer is three groups of 1/4 × 8. • Examples of problems grade five students should be able to solve include, but are not limited to the following:
• If nine children each bring 1/3 cup of candy for the party, how many thirds will there be? What will be the total number of cups of candy?
• If it takes 3/4 cup of ice cream to fill an ice cream cone, how much ice cream will be needed to fill eight cones?
• Resulting fractions should be expressed in simplest form.
• Problems where the denominator is not a factor of the whole number (e.g., 1/8 × 6 or 6 × 1/8 ) will be a focus in grade six.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Solve single-step and multistep practical problems involving addition and subtraction with fractions (proper or improper) having like and unlike denominators and/or mixed numbers. Denominators in the problems should be limited to 12 or less (e.g., 5/8 + 1/4 , 5/6 − 2/3 , 3 3/4 + 2 5/12) and answers should be expressed in simplest form.
• Solve single-step practical problems involving multiplication of a whole number, limited to 12 or less, and a proper fraction (e.g., 6 × 1/3, 1/4 × 8, 9 × 2/3 ), with models. The denominator will be a factor of the whole number and answers should be expressed in simplest form.
• Apply the inverse property of multiplication in models. (For example, use a visual fraction model to represent 4/4 or 1 as the product of 4 × 1/4).

### KEY VOCABULARY

Updated: Mar 06, 2019