Description I. The Structure and Calculation of Decimals 01 The Structure of Decimals 1. Decimals are made from 10 digits and place values less than 1. Writing decimals in base ten | The structure of decimals | The place value of decimals | Expanded form in base ten 2. Zeros can be added infinitely to the end of a decimal. Zeros at the end of a decimal 3. The higher the place value, the greater the value. Comparing the size of decimals 02 Calculating with Decimals 1. The decimal point is the reference for aligning decimal places. Addition and subtraction of decimals 2. A 1 in a higher place is a 10 in the place below. Addition with carrying, subtraction with borrowing | Zeros at the end of a decimal 3. ●.■ means there are ●■ copies of 0.1. (Decimal) × (Whole Number) 4. The decimal point shifts according to the number of decimal places being multiplied. The position of the decimal point in multiplication | × (Decimal) 5. Multiplying does not always make the value bigger. The relationship between the multiplier and the product's size 6. ●.■ means there are ●■ copies of 0.1. (Decimal) ÷ (Whole Number) 7. It is easier to divide by a whole number. The relationship between the dividend, divisor, and quotient | ÷ (Decimal) 8. Dividing does not always make the value smaller. The relationship between the divisor and the quotient's size 9. Zeros can be added infinitely to the end of a decimal. Bringing down zeros after the decimal point to calculate | Division where the decimal digits of the quotient continue endlessly | Terminating and non-terminating decimals 10. The remainder changes depending on the quotient. The quotient and remainder | The decimal point of the remainder II. The Structure and Calculation of Fractions 01 The Structure of Fractions 1. A fraction represents the portion a part takes up of the whole. Fractions | The value of a fraction of the whole 2. When the whole is 1, a fraction represents its own value. The value of a fraction 3. The value of a fraction equals the quotient of the numerator divided by the denominator. The relationship between fractions and division 4. The name of a fraction is determined by the size of the numerator and denominator. Proper and improper fractions | Mixed numbers | The relationship between improper fractions and mixed numbers 5. There are countless fractions with the same value. Equivalent fractions | Reducing fractions | Finding common denominators 6. The size of fractions is compared by making denominators or numerators equal. Comparing by equalizing denominators | Comparing by equalizing numerators 7. Writing a fraction in base ten turns it into a decimal. Expressing fractions as decimals (1) | Expressing fractions as decimals (2) | Expressing decimals as fractions | Comparing the size of fractions and decimals 8. Setting a standard allows comparison of the size of numbers. Ratio and rate | Percentage 02 Calculating with Fractions 1. The two numbers being added or subtracted are values; the number being multiplied is a rate. The principles of fraction addition and multiplication 2. Add and subtract the values of parts relative to the whole. Addition and subtraction of fractions with the same denominator 3. The value of a fraction is based on its denominator. Calculations with whole numbers and fractions | Addition and subtraction of fractions with carrying and borrowing 4. The reference must be the same in order to add or subtract values. Addition and subtraction of fractions with different denominators 5. When the value of a fraction is treated as the whole, find the fractional part. Multiplication of fractions | Multiplication of whole numbers and fractions | Multiplication of mixed numbers | Reciprocals 6. Division is multiplication by the reciprocal. Division of fractions