Mixed Calculations with Decimals

The rules that multiplication and division come first, and that parentheses come first of all, are confirmed through three-term chains of multiplication and division, expressions with parentheses, and the distributive law. Word problems combining addition with division, subtraction with multiplication and similar pairs give practice at putting a whole situation into a single expression.

Working 1.2 + 0.8 × 0.5 from left to right and answering 1 is the most frequent error, where the correct value is 1.6. In word problems the direction of the subtraction gets reversed, and answers turn up where the amount handed over is subtracted from the price when change was what the question wanted.

This unit is the stepping stone for grade 6, when Mixed Operations with Fractions and Decimals adds fractions into the mix. The four operations, gained one at a time up through Division of Decimals, are here made to combine freely within a single expression.