Solving inequalities with decimals

Comparing decimals is a place-value job: line up the points and read from the left until two digits differ. Here each side is a product, so your child multiplies first, then compares, and a few rows can be judged without multiplying at all.

Look at rows 3 and 8. Both sides are multiplied by the same number, 9 or 3, so only 89.0001 against 89.00011 and 113.1002 against 113.10003 matter. Four rows come out equal, like 8.96 × 4 and 17.92 × 2, which rewards spotting equal products by doubling and halving.

The standards are 6.NS.B.3 for the multiplication and 6.NS.C.7, ordering rational numbers, for the comparison.

Row 8 is the one to read aloud. Have your child point to each digit after the point, one place at a time. "Where do the two numbers first differ?" At the fourth place, a 2 against a 0.

The likely slip is exactly what the page tests: more digits look like a bigger number. Row 13 holds a gentler surprise. "What does any number times 0 make?"

A note for parents on row 8: the answer page shows less than, but 113.1002 × 3 = 339.3006 is greater than 113.10003 × 3 = 339.30009. The correct sign is greater than. Let your child find it; catching a mistake in a key is real proof of understanding.

Two packs of the same juice make a ready-made comparison: 3 bottles at $1.25 against 2 bottles at $1.80. Ask your child for the sign before anyone multiplies, then check.

After a run or a bike ride, compare two weeks as products: 2 rides of 1.6 miles against 3 rides of 1.05 miles.

In a game of Monopoly, before paying, compare two choices as products, such as three rents of $22 against two of $35, and say the sign out loud.

If your child caught row 8, say so: "You trusted place value over length." The next topic moves to fractions, starting with placing fractions on a number line.