MAT 156 topics for UNIT #4
7-1, 7-3, 7-2, 8-2, 7-4, 8-1
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7-1: Place Value:
- Place Value
- Write the name in words given a decimal
- Write the decimal number from the word name
between rational numbers in fraction and decimal form :
- Visual Manipulatives
- Base ten blocks (1, 1/10, 1/100)
- Money (dollar, dime and penny)
- Rational numbers can be written in 3 forms:
- Fractional form (no decimals allowed in fraction form)
- Decimal form (can terminate OR repeat - no fractions allowed in decimal form)
- percents (no repentends - bar- allowed in percent form)
- Rational numbers =
any number that CAN be written in its fraction form as
- Terminates in decimal form if the denominator has no factors other than 2 or 5.
- Repeats in decimal form if the denominator does have factors other than 2 or 5 (these are studied in 6-3)
- Decimal Fraction = -- ALWAYS TERMINATES in decimal form
- Be able to convert between fractions (to decimal fractions) to decimals that TERMINATE. Be able to tell ahead of time how many places it will terminate in.
- Be able to convert a terminating decimal back into a fraction in its most simplified form. Use the expanded notation form (by place value).
7-3: Repeating decimals:
- If the fraction cannot be written as a decimal fraction (if the denominator has factors other than 2 or 5) then it will REPEAT. Be able to write as a repeating decimal and label the REPETEND.
- Given a repeating decimal, use algebra to write the decimal as an exact fraction, in its simplest form.
- Be able to determine whether a rational number, given in its fractional form, will repeat or terminate as a decimal. If it will repeat, within how many places.
7-2: Decimal operations:
- Arithmetic (operations) on decimals- Be able to explain (or show proof for) all shortcuts on the four operations and be able to perform each with or without the shortcut (as decimal fractions).
- Addition -
- Be able to explain why you need to line up the decimals
- Subtraction -
- Be able to use equal addition and explain why it works
- Multiplication -
- Show why it works to just add up the number of decimal places and move it that many places for the final answer.
- Division -
- Show why it works to move the decimal place of the divisor and the dividend by the same amount.
- Definition : (per cent = per hundred)
- Be able to convert any rational number to its decimal, fraction and percent form
- convert fractions to percents and percents(must go through definition form: n/100) to fractions
- convert decimals to percents (must go through definition form: n/100) and percents to decimals
(fractions to decimals and reverse are done in 6-1 and 6-3)
- Solve simple equations of the form 25% of 8 is 2
7-4: Real numbers:
- Simplify radicals
- Discuss irrational numbers (like )
- never repeats or terminates as a decimal
(cannot be written as an exact decimal)
- cannot be written as a
- cannot be written as percents
- Solving proportions
- Solving applications involving proportions